Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour, what is his average rate for the entire trip in miles per minute?
A)1/8
B)2/15
C)3/15
D)1/4
E)3/8
OAA
Triathlete Dan
This topic has expert replies
-
- Legendary Member
- Posts: 510
- Joined: Thu Aug 07, 2014 2:24 am
- Thanked: 3 times
- Followed by:5 members
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi j_shreyans,
This is a "distance formula" question (that also involves average speed) that gives you all of the information that you need to answer the question, so you just have to plug the numbers into the formulas:
Distance = Rate x Time
Running:
2 miles = (10 miles/hr)(T)
2/10 = T
1/5 hour = Time to run
Swimming:
2 miles = (6 miles/hr)(T)
2/6 = T
1/3 hour = Time to swim
Total time = 1/5 + 1/3 = 8/15 hours
For this last series of steps, we have to pay very careful attention the specifics of the question. It asks for average rate in MILES PER MINUTE ( NOT miles per hour), so we'll have to do a little more work to get the answer.
Average Speed for the entire trip IN MILES PER MINUTE
Total Distance = (Average Speed) x (Total Time)
4 miles = (Av. Sp.)(8/15 hours)
4(15/8) = Av. Sp.
15/2 miles per HOUR = Av. Sp.
Since there are 60 minutes per hour, we have to divide this speed by 60...
(15/2)/60 = miles per MINUTE
1/8 miles per MINUTE
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This is a "distance formula" question (that also involves average speed) that gives you all of the information that you need to answer the question, so you just have to plug the numbers into the formulas:
Distance = Rate x Time
Running:
2 miles = (10 miles/hr)(T)
2/10 = T
1/5 hour = Time to run
Swimming:
2 miles = (6 miles/hr)(T)
2/6 = T
1/3 hour = Time to swim
Total time = 1/5 + 1/3 = 8/15 hours
For this last series of steps, we have to pay very careful attention the specifics of the question. It asks for average rate in MILES PER MINUTE ( NOT miles per hour), so we'll have to do a little more work to get the answer.
Average Speed for the entire trip IN MILES PER MINUTE
Total Distance = (Average Speed) x (Total Time)
4 miles = (Av. Sp.)(8/15 hours)
4(15/8) = Av. Sp.
15/2 miles per HOUR = Av. Sp.
Since there are 60 minutes per hour, we have to divide this speed by 60...
(15/2)/60 = miles per MINUTE
1/8 miles per MINUTE
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
Let's break it up into pieces. We'll change the rates to miles per minute by dividing each rate by 60.
Swimming:
D = 2
R = 1/10
Time = D/R = 2/(1/10) = 20 minutes
Running:
D = 2
R = 1/6
Time = D/R = 2/(1/6) = 12 minutes
He travels 4 miles in 32 minutes. This reduces to 1 mile in 8 minutes, or 1/8 of a mile per minute, so the answer is A.
Swimming:
D = 2
R = 1/10
Time = D/R = 2/(1/10) = 20 minutes
Running:
D = 2
R = 1/6
Time = D/R = 2/(1/6) = 12 minutes
He travels 4 miles in 32 minutes. This reduces to 1 mile in 8 minutes, or 1/8 of a mile per minute, so the answer is A.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
The distance traveled in each direction can be ANY VALUE.j_shreyans wrote:Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour, what is his average rate for the entire trip in miles per minute?
A)1/8
B)2/15
C)3/15
D)1/4
E)3/8
Let the distance in each direction = 30 miles.
At a rate of 10mph, the time spent running = d/r = 30/10 = 3 hours.
At a rate of 6mph, the time spent swimming = d/r = 30/6 = 5 hours.
Average rate for the entire trip = (total distance)/(total time) = (30+30)/(3+5) = 60/8 = 15/2 miles per hour.
Since 15/2 miles is traveled each hour, 1/60 of this distance is traveled each minute:
(1/60)(15/2) = 1/8 miles per minute.
The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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].
Student Review #1
Student Review #2
Student Review #3
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].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Average speed = (total distance)/(total time)j_shreyans wrote:Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour, what is his average rate for the entire trip in miles per minute?
A)1/8
B)2/15
C)3/15
D)1/4
E)3/8
OAA
We know the total distance = 4 miles
The total time consists of two parts:
Let's begin with a "word equation"
TOTAL time = (time spent running) + (time spent swimming)
time = distance/speed
So, time spent running = 2/10 = 1/5 hours = 12 minutes
time spent swimming = 2/6 = 1/3 hours = 20 minutes
TOTAL time = (12 minutes) + (20 minutes)
= 32 minutes
AVERAGE speed = (total distance)/(total time)
= (4 miles)/(32 minutes)
= 1/8 miles/minute
= A
Cheers,
Brent
- GMATinsight
- Legendary Member
- Posts: 1100
- Joined: Sat May 10, 2014 11:34 pm
- Location: New Delhi, India
- Thanked: 205 times
- Followed by:24 members
CONCEPT: AVERAGE SPEED = TOTAL DISTANCE / TOTAL TIMEj_shreyans wrote:Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour, what is his average rate for the entire trip in miles per minute?
A)1/8
B)2/15
C)3/15
D)1/4
E)3/8
OAA
Total Distance Traveled = 2 (Running) + 2 (Swimming) = 4 miles
Total Time (Distance/Speed) Taken = (2/10) (Running) + (2/6) (Swimming) = (6+10)/30 = 16/30 = 8/15
Average Speed = 4 / (8/15) = 15/2 (Miles/Hour)
Average Speed = (15/2) x (1/60) = 1/8 Miles/Minute
Answer: Option A
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
All of the above approaches are solid - but man, that's not at all how I would do this.
There is a MUCH easier way - but it takes some out of the box thinking.
The first thing is to remember that on problem solving you have a HUGE asset - the answer has to be one of the 5 options given to you.
So....
The first thing I'd do is convert each answer into miles per hour (easier to think about since the problem is already in mph - why make your life harder by converting into miles/min - SILLY! Don't do it!!!)
A) (1/8) * 60 = 60/8 = like 7.something (don't need to be accurate - it's actually 7.5 - but we are only looking for some quick rough math)
B) (2/15)*60 = (quick mental reduction leaves 2*(60/15) -> 2*4 = 8
C) similar to B -> 12
D) 60/4 = 15
E) 3 * answer A = so 21"ish"
Now, just VISUALIZE the problem right?
The answer just HAS to be between 10mph and 6mph for it to even be reasonable.
Therefore, eliminate C, D, E
Now, 8 mph is the average of 10 and 6, but that's too easy AND you know that on the 10mph leg of the trip - you'll get done faster - so the average speed should be closer to 6 than to 10. (Does that make sense to you?)
BAM!!!
A is the only answer left.
I friggin love the GMAT when it gives softballs like this - but you've got to frame the questions the right way.
Wanna learn how to take apart the test in this way? Shoot me a pm or email me at [email protected]
There is a MUCH easier way - but it takes some out of the box thinking.
The first thing is to remember that on problem solving you have a HUGE asset - the answer has to be one of the 5 options given to you.
So....
The first thing I'd do is convert each answer into miles per hour (easier to think about since the problem is already in mph - why make your life harder by converting into miles/min - SILLY! Don't do it!!!)
A) (1/8) * 60 = 60/8 = like 7.something (don't need to be accurate - it's actually 7.5 - but we are only looking for some quick rough math)
B) (2/15)*60 = (quick mental reduction leaves 2*(60/15) -> 2*4 = 8
C) similar to B -> 12
D) 60/4 = 15
E) 3 * answer A = so 21"ish"
Now, just VISUALIZE the problem right?
The answer just HAS to be between 10mph and 6mph for it to even be reasonable.
Therefore, eliminate C, D, E
Now, 8 mph is the average of 10 and 6, but that's too easy AND you know that on the 10mph leg of the trip - you'll get done faster - so the average speed should be closer to 6 than to 10. (Does that make sense to you?)
BAM!!!
A is the only answer left.
I friggin love the GMAT when it gives softballs like this - but you've got to frame the questions the right way.
Wanna learn how to take apart the test in this way? Shoot me a pm or email me at [email protected]
Want to 3x your study, time, and results on the GMAT?
Free report shows you how to get explosive growth on the GMAT.
Get it here:
https://bit.ly/GMATleverage
Free report shows you how to get explosive growth on the GMAT.
Get it here:
https://bit.ly/GMATleverage
Sorry, double post
Want to 3x your study, time, and results on the GMAT?
Free report shows you how to get explosive growth on the GMAT.
Get it here:
https://bit.ly/GMATleverage
Free report shows you how to get explosive growth on the GMAT.
Get it here:
https://bit.ly/GMATleverage
- GMATinsight
- Legendary Member
- Posts: 1100
- Joined: Sat May 10, 2014 11:34 pm
- Location: New Delhi, India
- Thanked: 205 times
- Followed by:24 members
If getting the quick answer is a concern then I would attempt this question by a straight concept
Average Speed when the distance is constant in to and fro motion = 2ab / (a+b) = 2x10x6 / (10+6) = 120/16 = 15/2 Miles/hour = 15/(2x60) Miles/Min = 1/8 Miles/Min
Answer: Option A
Time taken to solve : 10 Seconds
Average Speed when the distance is constant in to and fro motion = 2ab / (a+b) = 2x10x6 / (10+6) = 120/16 = 15/2 Miles/hour = 15/(2x60) Miles/Min = 1/8 Miles/Min
Answer: Option A
Time taken to solve : 10 Seconds
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We are given that Dan runs at a rate of 10 mph for 2 miles and then swims back the same 2 miles at a rate of 6 mph. Thus, Dan's running time is 2/10 = 1/5 of an hour and his swimming time is 2/6 = 1/3 of an hour.j_shreyans wrote:Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour, what is his average rate for the entire trip in miles per minute?
A)1/8
B)2/15
C)3/15
D)1/4
E)3/8
Now we can solve for his average rate:
average rate = (total distance)/(total time)
average rate = (2 + 2)/(1/5 + 1/3)
average rate = 4/(8/15) = 60/8 = 30/4 miles per hour (or 30 miles/4 hours)
Now we can convert this rate to minutes. Since 4 hours = 4 x 60 = 240 minutes, so the rate in miles per minute is:
30/240 = 1/8 mile per minute.
Answer: A
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews