CAT QUESTION: Triathlete Dan runs along a 2-mile stretch

[DianaN928]

How would I create a CONVERSION FACTOR for this? Trying to convert mph TO miles per minute mentally is hurting my brain...


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

[Sage Pearce-Higgins]

Haha! It does that to me too. Take care to apply an important principle of problem-solving: break things down into simple steps.

You know that 1 hour = 60 minutes.
Let's take an example: 15 miles per hour = 15 miles per 60 minutes
Now, that's a kind of ratio, 15 miles : 60 minutes
We can transform that ratio in the usual way, by multiplying or dividing both sides by the same number.
For example, it could be 7.5 miles : 30 minutes
Or, more usefully, 15/60 miles : 1 minute
That makes 1/4 mile per minute.

See if you can apply this idea to that problem.

[vaibhavs570]

the formula for average rate is 2ab/a+b
where a = distance that dan runs & b = distance that dan swims
So Average rate = 2*10*6/10+6 = 15/2 miles per hour
Since the rate in 60 minutes (1 hour) = 15/2
So in 1 minute the rate will be 15/2*1/60 = 1/8
IMO Answer is A

I hope it helps.

[Sage Pearce-Higgins]

Thanks for adding that solution. However, watch out when using formulas to solve problems - GMAT loves to make things a little bit different for each question, so memorizing formulas is often not as safe as being able to understand new situations.