Problem Solving

AAPL wrote:Official Guide

A driver completed the first 20 miles of a 40 miles trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-miles trip? (Assume that the driver did not make any stops during the 40-miles trip)

A. 65
B. 68
C. 70
D. 75
E. 80

OA D

Say the average speed the driver clocks for the remaining 20 miles to achieve an average speed of 60 miles per hour = x miles per hour

The average speed of the 40 miles = Total distance / Total time = 40 / (20/50 + 20/x)

60 = 40 / (20/50 + 20/x)

20/50 + 20/x = 40/60

2/5 + 20/x = 2/3

20/x = 2/3 - 2/5

x/20 = 4/16

x = 75 mph

The correct answer: D

Hope this helps!

-Jay
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AAPL wrote:Official Guide

A driver completed the first 20 miles of a 40 miles trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-miles trip? (Assume that the driver did not make any stops during the 40-miles trip)

A. 65
B. 68
C. 70
D. 75
E. 80

We can use the following formula:

average rate = (distance 1 + distance 2)/(time 1 + time 2)

where average rate = 60, distance 1 = distance 2 = 20, time 1 = distance 1/rate 1 = 20/50 = 2/5, and time 2 = distance 2/rate 2 = 20/r (where r is the average speed of the remaining 20 miles).

Let's now determine r:

60 = (20 + 20)/(2/5 + 20/r)

60 = 40/(2r/5r + 100/5r)

60 = 40/[(2r + 100)/5r]

60 = 200r/(2r + 100)

60(2r + 100) = 200r

120r + 6000 = 200r

6000 = 80r

r = 6000/80 = 600/8 = 75

Alternate Solution:

In order to achieve an average speed of 60 mph, the driver must complete the entire journey in 40/60 = 2/3 hours. Note that he already spent 20/50 = 2/5 hours on the first 20 miles of the trip; thus he must complete the remaining 20 miles in 2/3 - 2/5 = 4/15 hours. To travel 20 miles in 4/15 hours, his rate must be 20/(4/15) = (20 * 15)/4 = 5 * 15 = 75 mph.

Answer: D