A cyclist travels 20 miles at a speed of 15 miles per hour.

Question

A cyclist travels 20 miles at a speed of 15 miles per hour. If he returns along the same path and the entire trip takes 2 hours, at what speed did he return?

(A) 15 mph 
(B) 20 mph 
(C) 22 mph 
(D) 30 mph 
(E) 34 mph

KarishmaB · Accepted Answer

Let me add another method: Use logic!

He travels 20 miles at a speed of 15 mph so he takes 20/15 = 4/3 hrs to travel one way. Since total time is 2 hrs, he must have taken 2 - 4/3 = 2/3 hrs while returning.
Speed while returning = 20/(2/3) = 30 mph

(It's pretty much what cyberjadugar did but thinking in terms of equations can be a little frustrating during the test.)

cyberjadugar · Answer

Hi,

we know that  speed = \frac {distance}{time} 
 time(2hours) = \frac {20}{15}+\frac {20}{v} 
or  v= \frac {20}{2- \frac 43} 
or  v= 30

Thus, Answer (D)

Regards,

KapTeacherEli · Answer

Cyberjadugar's math is dead on!

There is another way to approach this problem, however--backsolving. Because the answers are numbers in ascending order, and because the task we are assigned is simple (not the same as easy! A speed is simple, the sum of the squares of two speeds would be complex), we can plug those numbers back into the task to see if they work.

With backsolving, it's useful to start at B or D. This maximized our chances of getting the answer right on the first try. If B is too big, or if D is too small, then we immediately know that A or E is correct, respectively.

But B clearly doesn't work here. The total distance traveled is 40 miles, and the total time is two hours. The average speed for the  whole  trip needs to be 40/2 = 20 mph, so 20 for only the second half won't cut it.

Let's try (D). 20 miles at 15 miles/hour takes 4/3 of an hour. 20 miles at (D) 30 miles/hour takes half that time, 2/3 of an hour. So the whole trip takes 6/3 = 2 hours, just what we wanted!

You may think, "How lucky!" but actually luck played no part. After all, what if we'd been wrong? Well, if we'd spend too little time making the trip, we'd have known that 30 was too fast. Since 20 was too slow, we could have marked (C) as correct without doing a bit of math! And similarly, if we'd been to slow even at 30, we could have just mark (E) and been done. Part of the power of backsolving as a strategy is the ability to use the answer choices as a powerful problem-solving tool.

Good luck on your prep!

BrushMyQuant · Answer

A cyclist travels 20 miles at a speed of 15 miles per hour

Time taken while going= Distance/Speed = 20/15 hrs = (4/3)hrs

Total time = 2hours

Time taken while returning = total - time taken while going = 2 - 4/3 = (2/3)hrs

Distance = 20miles
Time = (2/3)hrs

Speed = Distance/Time = 20/ (2/3) = 30 miles/hr

So, Answer is D (30mph)

Hope it helps!

JeffTargetTestPrep · Answer

We know that distance/rate = time. If we let the speed of the return trip = r, then our equation for the time for the entire trip is:

time going + time returning = 2 hours

20/15 + 20/r = 2

4/3 + 20/r = 2

Multiplying by 3r, we have:

4r + 60 = 6r

60 = 2r

30 = r

Answer: D

Nipungupta9081 · Answer

Making a matrix will help in this question.

bumpbot · Answer

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A cyclist travels 20 miles at a speed of 15 miles per hour.

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A cyclist travels 20 miles at a speed of 15 miles per hour.

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