16. A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph
Answer is (B)
Source: GMAT test code 14
I still have problems grasping the answer
Difficult Rates question
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Hi Gustavo,
Here is an explanation, let me know if it is not clear:
Average speed = distance/time
from time condition: t2 - t1 = 2 & t2 + t1 = 18; solve for t1: t1 = 8
from distance condition: s1 + s2 = 64; i.e., s2 = 64 - s1
from av. speed condition: v2 - v1 = 1, i.e., (s2/t2) - (s1/t1) = 1
replace value of t2, t1, s2 in this equation: (64-s1)/10 - (s1/8) = 1
solve for s1: s1 = 24
hence v1 = 24/8 = 3 mph ANSWER.
Here is an explanation, let me know if it is not clear:
Average speed = distance/time
from time condition: t2 - t1 = 2 & t2 + t1 = 18; solve for t1: t1 = 8
from distance condition: s1 + s2 = 64; i.e., s2 = 64 - s1
from av. speed condition: v2 - v1 = 1, i.e., (s2/t2) - (s1/t1) = 1
replace value of t2, t1, s2 in this equation: (64-s1)/10 - (s1/8) = 1
solve for s1: s1 = 24
hence v1 = 24/8 = 3 mph ANSWER.
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Hey Gustavo,
I thought of it like this. First, let's consider Day 1 and Day 2's hours.
If x = hours on Day 1, then x + 2 = hours on Day 2. The question said he walked 18 hours total, so we can set up a simple equation:
x + (x + 2) = 18
2x + 2 = 18
2x = 16
x = 8
Therefore he walked 8 hours on Day 1 and 10 hours on Day 2.
We are told he went 1mph FASTER on Day 2. So if Day 1's mph is y, then Day 2's mph is y + 1.
Let's look at the D = R x T formula.
D1 = R1 x T1
D2 = R2 x T2
If we plug in what we know:
D1 = (y) x 8 hrs
D2 = (y + 1) x 10 hrs
We know that D1 + D2 must equal 64, so we can sum the two equations and set them equal to 64.
(y) x 8hrs + (y + 1) x 10hrs = 64
Simplifying...
64 = 8y + 10y + 10
64 = 18y + 10
54 = 18y
3 = y
Hope this is clear!
Best,
Vivian
I thought of it like this. First, let's consider Day 1 and Day 2's hours.
If x = hours on Day 1, then x + 2 = hours on Day 2. The question said he walked 18 hours total, so we can set up a simple equation:
x + (x + 2) = 18
2x + 2 = 18
2x = 16
x = 8
Therefore he walked 8 hours on Day 1 and 10 hours on Day 2.
We are told he went 1mph FASTER on Day 2. So if Day 1's mph is y, then Day 2's mph is y + 1.
Let's look at the D = R x T formula.
D1 = R1 x T1
D2 = R2 x T2
If we plug in what we know:
D1 = (y) x 8 hrs
D2 = (y + 1) x 10 hrs
We know that D1 + D2 must equal 64, so we can sum the two equations and set them equal to 64.
(y) x 8hrs + (y + 1) x 10hrs = 64
Simplifying...
64 = 8y + 10y + 10
64 = 18y + 10
54 = 18y
3 = y
Hope this is clear!
Best,
Vivian
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Total time = 18 hours.gustavo.taucei wrote:16. A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph
Answer is (B)
Source: GMAT test code 14
I still have problems grasping the answer
Since the hiker walked 2 hours longer on the second day, time on the first day = 8 hours, time on the second day = 10 hours.
Now we can plug in the answer choices, which represent the speed on the first day.
Answer choice C: Rate on the first day = 4 mph
Distance on first day = r*t = 4*8 = 32 miles.
Rate on the second day = 4+1 = 5 mph.
Distance on the second day = r*t = 5*10 = 50 miles.
Total distance = 32+50 = 82 miles.
The rate is too fast. Eliminate C, D and E.
Answer choice B: Rate on the first day = 3 mph
Distance on first day = r*t = 3*8 = 24 miles.
Rate on the second day = 3+1 = 4 mph.
Distance on the second day = r*t = 4*10 = 40 miles.
Total distance = 24+40 = 64 miles. Success!
The correct answer is B.
Last edited by GMATGuruNY on Wed Sep 07, 2011 4:40 pm, edited 1 time in total.
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IMO B
Are these retired test code papers good practice ?
I have a couple with me.
Are these retired test code papers good practice ?
I have a couple with me.
Cheers !!
Quant 47-Striving for 50
Verbal 34-Striving for 40
My gmat journey :
https://www.beatthegmat.com/710-bblast-s ... 90735.html
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https://www.beatthegmat.com/ways-to-bbla ... 90808.html
How to prepare before your MBA:
https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_
Quant 47-Striving for 50
Verbal 34-Striving for 40
My gmat journey :
https://www.beatthegmat.com/710-bblast-s ... 90735.html
My take on the GMAT RC :
https://www.beatthegmat.com/ways-to-bbla ... 90808.html
How to prepare before your MBA:
https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_
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Mitch, would a weighted average approach help in tackling such problems in case of time crunch?GMATGuruNY wrote:Total time = 18 hours.gustavo.taucei wrote:16. A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph
Answer is (B)
Source: GMAT test code 14
I still have problems grasping the answer
Since the hiker walked 2 hours longer on the second day, time on the first day = 8 hours, time on the second day = 10 hours.
Now we can plug in the answer choices, which represent the speed on the first day.
Answer choice C: Rate on the first day = 4 mph
Distance on first day = r*t = 4*8 = 32 miles.
Rate on the second day = 4+1 = 5 mph.
Distance on the second day = r*t = 5*10 = 50 miles.
Total distance = 32+50 = 82 miles.
The rate is too fast. Eliminate C, D and E.
Answer choice B: Rate on the first day = 3 mph
Distance on first day = r*t = 3*8 = 24 miles.
Rate on the second day = 3+1 = 4 mph.
Distance on the second day = r*t = 4*10 = 40 miles.
Total distance = 24+40 = 64 miles. Success!
The correct answer is B.
Realising that the question by itself provides TOTAL DISTANCE and TOTAL TIME made me treat this as a WA problem without using a Chart.
Here the WA is 3.55. Given that the answer choices are only 1 mile/hour apart, this WA falls between 3 mph and 4 mph. Also, since the weight here is time, Day 2 has more weight as the hiker walked 2 hours longer.
Thus, the answer is 4 mph? Can i do it this way?
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Sorry TYPO error! the answer is 3 mph as the weight of the 1st day is lesser!Jayanth2689 wrote:Mitch, would a weighted average approach help in tackling such problems in case of time crunch?GMATGuruNY wrote:Total time = 18 hours.gustavo.taucei wrote:16. A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph
Answer is (B)
Source: GMAT test code 14
I still have problems grasping the answer
Since the hiker walked 2 hours longer on the second day, time on the first day = 8 hours, time on the second day = 10 hours.
Now we can plug in the answer choices, which represent the speed on the first day.
Answer choice C: Rate on the first day = 4 mph
Distance on first day = r*t = 4*8 = 32 miles.
Rate on the second day = 4+1 = 5 mph.
Distance on the second day = r*t = 5*10 = 50 miles.
Total distance = 32+50 = 82 miles.
The rate is too fast. Eliminate C, D and E.
Answer choice B: Rate on the first day = 3 mph
Distance on first day = r*t = 3*8 = 24 miles.
Rate on the second day = 3+1 = 4 mph.
Distance on the second day = r*t = 4*10 = 40 miles.
Total distance = 24+40 = 64 miles. Success!
The correct answer is B.
Realising that the question by itself provides TOTAL DISTANCE and TOTAL TIME made me treat this as a WA problem without using a Chart.
Here the WA is 3.55. Given that the answer choices are only 1 mile/hour apart, this WA falls between 3 mph and 4 mph. Also, since the weight here is time, Day 2 has more weight as the hiker walked 2 hours longer.
Thus, the answer is 4 mph? Can i do it this way?
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Nice work!Jayanth2689 wrote:Sorry TYPO error! the answer is 3 mph as the weight of the 1st day is lesser!Jayanth2689 wrote:Mitch, would a weighted average approach help in tackling such problems in case of time crunch?GMATGuruNY wrote:Total time = 18 hours.gustavo.taucei wrote:16. A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph
Answer is (B)
Source: GMAT test code 14
I still have problems grasping the answer
Since the hiker walked 2 hours longer on the second day, time on the first day = 8 hours, time on the second day = 10 hours.
Now we can plug in the answer choices, which represent the speed on the first day.
Answer choice C: Rate on the first day = 4 mph
Distance on first day = r*t = 4*8 = 32 miles.
Rate on the second day = 4+1 = 5 mph.
Distance on the second day = r*t = 5*10 = 50 miles.
Total distance = 32+50 = 82 miles.
The rate is too fast. Eliminate C, D and E.
Answer choice B: Rate on the first day = 3 mph
Distance on first day = r*t = 3*8 = 24 miles.
Rate on the second day = 3+1 = 4 mph.
Distance on the second day = r*t = 4*10 = 40 miles.
Total distance = 24+40 = 64 miles. Success!
The correct answer is B.
Realising that the question by itself provides TOTAL DISTANCE and TOTAL TIME made me treat this as a WA problem without using a Chart.
Here the WA is 3.55. Given that the answer choices are only 1 mile/hour apart, this WA falls between 3 mph and 4 mph. Also, since the weight here is time, Day 2 has more weight as the hiker walked 2 hours longer.
Thus, the answer is 4 mph? Can i do it this way?
The answer choices represent the slower speed.
The average speed for the entire trip = 64/18 ≈ 3.5.
Thus, the slower speed must be LESS than 3.5 miles per hour and the faster speed must be GREATER than 3.5 miles per hour.
The problem states that the difference between the two speeds is 1 mile per hour.
Thus, only answer choice B-- which implies a slower speed of 3 miles per hour and a faster speed of 4 miles per hour -- is viable.
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Thanks Mitch!!GMATGuruNY wrote:Nice work!Jayanth2689 wrote:Sorry TYPO error! the answer is 3 mph as the weight of the 1st day is lesser!Jayanth2689 wrote:Mitch, would a weighted average approach help in tackling such problems in case of time crunch?GMATGuruNY wrote:Total time = 18 hours.gustavo.taucei wrote:16. A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph
Answer is (B)
Source: GMAT test code 14
I still have problems grasping the answer
Since the hiker walked 2 hours longer on the second day, time on the first day = 8 hours, time on the second day = 10 hours.
Now we can plug in the answer choices, which represent the speed on the first day.
Answer choice C: Rate on the first day = 4 mph
Distance on first day = r*t = 4*8 = 32 miles.
Rate on the second day = 4+1 = 5 mph.
Distance on the second day = r*t = 5*10 = 50 miles.
Total distance = 32+50 = 82 miles.
The rate is too fast. Eliminate C, D and E.
Answer choice B: Rate on the first day = 3 mph
Distance on first day = r*t = 3*8 = 24 miles.
Rate on the second day = 3+1 = 4 mph.
Distance on the second day = r*t = 4*10 = 40 miles.
Total distance = 24+40 = 64 miles. Success!
The correct answer is B.
Realising that the question by itself provides TOTAL DISTANCE and TOTAL TIME made me treat this as a WA problem without using a Chart.
Here the WA is 3.55. Given that the answer choices are only 1 mile/hour apart, this WA falls between 3 mph and 4 mph. Also, since the weight here is time, Day 2 has more weight as the hiker walked 2 hours longer.
Thus, the answer is 4 mph? Can i do it this way?
The answer choices represent the slower speed.
The average speed for the entire trip = 64/18 ≈ 3.5.
Thus, the slower speed must be LESS than 3.5 miles per hour and the faster speed must be GREATER than 3.5 miles per hour.
The problem states that the difference between the two speeds is 1 mile per hour.
Thus, only answer choice B-- which implies a slower speed of 3 miles per hour and a faster speed of 4 miles per hour -- is viable.