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Alice travels 120 km, the first 40 km at x km/h and the rema

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Alice travels 120 km, the first 40 km at x km/h and the rema

by Max@Math Revolution » Fri Jul 20, 2018 12:17 am

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[GMAT math practice question]

Alice travels 120 km, the first 40 km at x km/h and the remaining 80 km at y km/h. What is her average speed for the entire trip?

A. 2xy/(2x+y)
B. 2xy/(3x+y)
C. 3xy/(2x+y)
D. xy/(2x+y)
E. xy/(x+2y)
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by swerve » Fri Jul 20, 2018 10:11 am
I think that an easy way to solve this PS questions is as follows,

. . . . . . . . . . . . . . Distance . . . . . . . . . . . . Rate . . . . . . . . . . . . . . Time
. . . . . . . . . . . . . . . .40km . . . . . . . . . . . . . x km/h . . . . . . . . . . . . . 40/x
. . . . . . . . . . . . . . . .80km . . . . . . . . . . . . . y km/h . . . . . . . . . . . . . 80/y
--------------------------------------------------------------------------
Total . . . . . . . . . .120km . . . . . . . . . . . . . {---} . . . . . . . . . . (40y + 80x)/ (xy)

To calculate rate: 120*(xy/(40y + 80x)) = 3xy/(y + 2x)

Hence, the correct answer is C. Regards!
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by Max@Math Revolution » Sun Jul 22, 2018 5:06 pm
=>

The average speed is (Total Distance) / (Total Time).
The time for the first 40 km is 40 / x and the time for the remaining 80 km is 80 / y. Thus, the total time for the trip is ( 40/x + 80/y ).
Her average speed for the trip is
120 / ( 40/x + 80/y ) = 120xy / ( 40y + 80x ) = 3xy / ( y + 2x ) = 3xy /
(2x +y).

Therefore, the answer is C.
Answer : C
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by Scott@TargetTestPrep » Mon Jul 23, 2018 5:16 pm
Max@Math Revolution wrote:[GMAT math practice question]

Alice travels 120 km, the first 40 km at x km/h and the remaining 80 km at y km/h. What is her average speed for the entire trip?

A. 2xy/(2x+y)
B. 2xy/(3x+y)
C. 3xy/(2x+y)
D. xy/(2x+y)
E. xy/(x+2y)
We can use the average rate formula: average rate = total distance/total time

Average rate = 120/(40/x + 80/y)

Average rate = 120/(40y/xy + 80x/xy)

Average rate = 120/[(40y + 80x)/xy]

Average rate = 120xy/(40y + 80x)

Average rate = 120xy/40(y + 2x) = 3xy/(y + 2x)

Answer: C

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