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Traveling Round trip

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Traveling Round trip

by oquiella » Sat Oct 10, 2015 1:01 pm
A car travels from Mayville to Rome at an average speed of 30 mph and returns immediately along the same route at an average speed of 40 mph. Or the following, which is closest to the average speed, in miles per hour, for the round trip?

A. 32
B. 33
C. 34.3
D. 35.5
E. 36.5


Please explain why.
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by theCEO » Sat Oct 10, 2015 1:12 pm
oquiella wrote:A car travels from Mayville to Rome at an average speed of 30 mph and returns immediately along the same route at an average speed of 40 mph. Or the following, which is closest to the average speed, in miles per hour, for the round trip?

A. 32
B. 33
C. 34.3
D. 35.5
E. 36.5


Please explain why.
x = distance one way

avg speed round trip = total distance / total time

total distance = x + x = 2x

total time = x/30 + x/40 = 7x/120

total distance / total time = 2x (120/7x) = 34.3

ans = c
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by GMATGuruNY » Sat Oct 10, 2015 1:24 pm
oquiella wrote:A car travels from Mayville to Rome at an average speed of 30 mph and returns immediately along the same route at an average speed of 40 mph. Or the following, which is closest to the average speed, in miles per hour, for the round trip?

A. 32
B. 33
C. 34.3
D. 35.5
E. 36.5
Let the distance in each direction = 120 miles.
Time to travel to Rome at 30mph = d/r = 120/30 = 4 hours.
Time to travel to Mayville at 40mph = d/r = 120/40 = 3 hours.
Average speed = (total distance)/(total time) = (120+120)/(4+3) = 240/7 = a little more than 34mph.

The correct answer is C.
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by Brent@GMATPrepNow » Sat Oct 10, 2015 2:34 pm
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round-trip?

(A) 32.0 (B) 33.0 (C) 34.3 (D) 35.5 (E) 36.5
We can solve this one quickly if we assign a "nice" distance between Mayville and Rome ("nice" means a distance that works well with 30 miles per hour AND 40 miles per hour)

So, let's say the distance between Mayville and Rome = 120 miles

Time = distance/speed
So, time from Mayville and Rome (at 30 mph) = 120/30 = 4 hours
Time from Rome to Mayville (at 40 mph) = 120/40 = 3 hours

Average speed = (total distance traveled)/(total time)
= (120 + 120)/(4 + 3)
= 240/7
= 34.something (if we use long division here, we'll stop once we get to the ones digit)
= C

Cheers.
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