PS

[ketkoag]

A driver completed the first 20 miles of a 40-mile 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-mile trip? (Assume that the driver did not make any stops during the 40-mile trip.)
A. 65 mph
B. 68 mph
C. 70 mph
D. 75 mph
E. 80 mph

OA: D
Please explain how to solve it, coz by using average speed = total distance/ total time i am not able to get the right answer. it seems to be easy one.
please explain..

[moutar]

20 miles @ 50mph = 24 mins

Trip needs to be done in 40 mins (40 miles @ 60mph)

Therefore 20 miles in 16 mins = 20/(4/15)
= 15 x 5
= 75mph

[kaf]

We know that Average Speed (AS) = Total Distance / Total Time.

We also know that AS = 2(S1 * S2) / S1 + S2 where

S1 is the speed for the first half of the trip and
S2 is the speed for the second half of the trip

We wont to attain an AS = 60mph for the entire 40 mile trip.

therefore

60 = 2(50 * S2) / (50 + S2)

60(50 + S2) = 2(50 * S2) <------- Cross multiplication

3000 + 60S2 = 100S2

3000 = 100S2 - 60S2

3000 = 40S2

3000 / 40 = S2

75 = S2