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A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed...

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by BTGmoderatorLU » Wed Apr 15, 2020 4:58 am

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Source: GMAT Paper Tests

A hiker walked for two days. On the second day, the hiker walked 2 hours longer and at an average speed of 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

The OA is B
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Re: A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed...

by Brent@GMATPrepNow » Wed Apr 15, 2020 6:21 am
BTGmoderatorLU wrote: ↑
Wed Apr 15, 2020 4:58 am
 Source: GMAT Paper Tests

A hiker walked for two days. On the second day, the hiker walked 2 hours longer and at an average speed of 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

The OA is B
If we let x = the hiker's walking speed on day 1, then x+1 = the hiker's walking speed on day 2 (since the hiker walked 1 mph faster on the second day)
So, the hiker's AVERAGE speed will be BETWEEN x and x+1 mph

The hiker walked 64 miles and 18 hours.
Average speed = distance/time = 64/18 ≈ 3.5 mph

So, according to the above property, it must be the case that x = 3 mph, and x+1 = 4 mph

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed...

by swerve » Wed Apr 15, 2020 2:32 pm
BTGmoderatorLU wrote: ↑
Wed Apr 15, 2020 4:58 am
 Source: GMAT Paper Tests

A hiker walked for two days. On the second day, the hiker walked 2 hours longer and at an average speed of 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

The OA is B
Let \(x\) be the number of miles in first day; \(64-x =\) number of miles in second day
given,
\(t+ t+2 =18 \Rightarrow t=10\)

Speed in the first day \(=\) speed in the second day \(- 1\)

Therefore, \(\dfrac{64−x}{10} -\dfrac{x}{8} = 1\)

\(x = 24\)

Therefore, speed \(= \dfrac{d}{t} = \dfrac{24}{8} = 3\)
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Re: A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed...

by Scott@TargetTestPrep » Fri Apr 17, 2020 3:32 am
BTGmoderatorLU wrote: ↑
Wed Apr 15, 2020 4:58 am
 Source: GMAT Paper Tests

A hiker walked for two days. On the second day, the hiker walked 2 hours longer and at an average speed of 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

The OA is B
We can let t = the number of hours and r = the speed he walked on the first day. We can create the equations:

t + t + 2 = 18

and

tr + (t +2)(r + 1) = 64

Solving the first equation, we have:

2t = 16

t = 8

Now, substituting t = 8 into the second equation, we have:

8r + 10(r + 1) = 64

8r + 10r + 10 = 64

18r = 54

r = 3

Answer: B

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