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# Tavi drives 113 miles at 50 miles per hour and returns

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Tavi drives 113 miles at 50 miles per hour and returns [#permalink]  20 Oct 2017, 16:05
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Question Stats:

65% (01:02) correct 34% (00:19) wrong based on 38 sessions

Tavi drives 113 miles at 50 miles per hour and returns via the same route at 60 miles per hour.

 Quantity A Quantity B Tavi's average speed for the entire round trip 55 mph

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: Tavi drives 113 miles at 50 miles per hour and returns [#permalink]  21 Oct 2017, 07:11
Here is the trick, the average speed is not computed as a usual average, which would have lead to a wrong answer (C).

It is computed as $$\bar{speed} = \frac{distance_1+distance_2}{time_1+time_2}$$. In our case, the distances are equal since the trip is one way and the other, i.e. 113 + 113 = 226 miles, while the time spent is computed as 113/50 = 2.6 hours and 113/60 = 1.883 hours. Substituting in the formula the average speed is 50.41.

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Re: Tavi drives 113 miles at 50 miles per hour and returns [#permalink]  11 Mar 2018, 07:17
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Re: Tavi drives 113 miles at 50 miles per hour and returns [#permalink]  12 Mar 2018, 19:32
1st leg: t1 = 113/50
2nd leg: t2 = 113/60

Total time = t1 + t2 = 113/50 + 113/60

Average speed for the round trip = Total distance/Total time = (113 + 113)/(113/50 + 113/60) = 54.5 mph < 55 mph.

So Ans: B
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Re: Tavi drives 113 miles at 50 miles per hour and returns [#permalink]  13 Mar 2018, 15:49
correct: B
route = 113 miles (50 miles / hour) 113/50 hours
return_route = 113 miles (60 miles /hour) 113 / 60 hours
his average speed is: total miles passed / total time passed = (113 + 113)/ (113/50 + 113/60) = 226 * 300/ 1243 = 54.4
average_speed = 54.4 miles per hour
so B is bigger than A

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Re: Tavi drives 113 miles at 50 miles per hour and returns   [#permalink] 13 Mar 2018, 15:49
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# Tavi drives 113 miles at 50 miles per hour and returns

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