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Triathlete Dan

by j_shreyans » 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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by [email protected] » Sun Oct 12, 2014 11:24 am
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

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by Matt@VeritasPrep » Sun Oct 12, 2014 8:56 pm
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.
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by GMATGuruNY » 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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by Brent@GMATPrepNow » 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

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by GMATinsight » 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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by Joey N » 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.


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by Joey N » Wed Oct 15, 2014 4:49 am
Sorry, double post
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by GMATinsight » 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 :lol:
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by Scott@TargetTestPrep » 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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