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Triathlete Dan runs along a 2-mile stretch of river and then swims bac

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Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Oct 2014, 08:15, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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New post 24 Dec 2007, 05:20
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Dan travels 4 miles round trip.

Running part: (2/10 = 1/5*60 = 12 minutes)
Swimming Part: (2/6 = 1/3*60 = 20 minutes)

4 miles in (12+20) minutes
4/32 = 1/8 mile per minute

Answer: 1/8 mile per minute

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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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New post 24 Dec 2007, 06:16
dynamo 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?


Total Distance/Total time

=4/ [( 1/5) + (1/3)]= 15/2

in miles per minute 15/2*60 = 1/8

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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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New post 24 Dec 2007, 16:48
time to run = 1/5 hr = 12 minutes

time to swim = 1/3 hr = 20 minutes

average rate = total distance / total time
= 4 miles / 20+12 = 4/32 = 1/8 mile per minute

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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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If distance traveled is same but at varying rates, the average rate can be found through the shortcut \(\frac{2ab}{a+b}\) where a and b are individual rates.
In this problem \(a=10\) and \(b=6\) therefore average speed = \(\frac{15}{2}\) miles per hour, i.e. \(\frac{1}{8}\) miles per minute.

P.S. Added tags as saw this question in an MGMAT CAT.

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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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New post 15 Sep 2014, 01:03
Dienekes wrote:
If distance traveled is same but at varying rates, the average rate can be found through the shortcut \(\frac{2ab}{a+b}\) where a and b are individual rates.
In this problem \(a=10\) and \(b=6\) therefore average speed = \(\frac{15}{2}\) miles per hour, i.e. \(\frac{1}{8}\) miles per minute.

P.S. Added tags as saw this question in an MGMAT CAT.


Can you kindly update OA for this?

Thanks
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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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New post 17 Nov 2015, 15:32
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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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New post 13 Jan 2017, 15:54
Hello from the GMAT Club BumpBot!

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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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New post 18 Jan 2017, 09:56
dynamo 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


t1 = 2/10 hours
t2 = 2/6

t =t1 + t2 = 2/10 + 2/6 = 16/30

Average speed = Total distance/ total time = 4/ [16/30] = 15/2 mph

15/2 * 1/60 = 1/8 miles/min

Ans.: A

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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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New post 19 Apr 2017, 23:24
dynamo 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 can approach this problem using conversion factors

If the total distance is 2 miles and Dan runs at a rate of 10 miles per hour then he will cover in 1/5 of an hour or 1 mile in 6 minutes

1 mile/6 minutes = 2 miles/ 20 minutes

cross multiply add and then divide by 2

(16 miles /2) / 60 minutes

(16 miles/2)/ 1 minute

8 miles/ 1 minute

1 minute/ 8 miles

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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]

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New post 01 Aug 2017, 02:38
Dienekes wrote:
If distance traveled is same but at varying rates, the average rate can be found through the shortcut \(\frac{2ab}{a+b}\) where a and b are individual rates.
In this problem \(a=10\) and \(b=6\) therefore average speed = \(\frac{15}{2}\) miles per hour, i.e. \(\frac{1}{8}\) miles per minute.

P.S. Added tags as saw this question in an MGMAT CAT.


Thank you for the explanation. I picked answer choice "B" because I did not pay attention to the unit (minutes) in the question.

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Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac   [#permalink] 01 Aug 2017, 02:38
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