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Triathlete Dan

This topic has 5 expert replies and 4 member replies
j_shreyans Legendary Member Default Avatar
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Triathlete Dan

Post Sun Oct 12, 2014 8:06 am
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

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Joey N Newbie | Next Rank: 10 Posts Default Avatar
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Post Wed Oct 15, 2014 4:49 am
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 joey@strategicgmat.com

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Joey N Newbie | Next Rank: 10 Posts Default Avatar
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Post Wed Oct 15, 2014 4:49 am
Sorry, double post

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Joey N Newbie | Next Rank: 10 Posts Default Avatar
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Post Wed Oct 15, 2014 4:49 am
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 joey@strategicgmat.com

_________________
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:
http://bit.ly/GMATleverage

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Joey N Newbie | Next Rank: 10 Posts Default Avatar
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Post Wed Oct 15, 2014 4:49 am
Sorry, double post

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GMAT/MBA Expert

Post Wed Dec 13, 2017 4:52 pm
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
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.

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

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Post Wed Oct 15, 2014 7:49 am
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 Laughing

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Post Wed Oct 15, 2014 4:08 am
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
CONCEPT: AVERAGE SPEED = TOTAL DISTANCE / TOTAL TIME

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

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Post Tue Oct 14, 2014 8:42 am
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
Average speed = (total distance)/(total time)
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

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Post Mon Oct 13, 2014 2:45 am
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
The distance traveled in each direction can be ANY VALUE.
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.

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