You plan a car trip for which you want to average 90 km/h. You cover the first half of the distance at an average speed of only 48 km/h. What must your average speed be in the second half of the trip to meet your goal? Not that the velocities are based on half the distance, not half the time.

Question

anonymous · Answer

720 km/h
Better hurry...

anonymous · Answer

how did you figure this out?

anonymous · Answer

Say S is half the distance, V1, V2 and Vtot the speeds, T1, T2 and Ttot the times.

anonymous · Answer

You know V1=48 km/h and Vtot=90km/h

anonymous · Answer

T1=S/V1
T2=Ttot-T1=(2S/Vtot)-S/V1
V2=S/T2 = S / (2S/Vtot-S/V1)

anonymous · Answer

Simplify in V2 = V1Vtot/(2V1-Vtot) = 48 * 90 / 6 = 720

anonymous · Answer

Interestingly, there is only a real solution if V1>45.
For V1=45, you're only half way in the time you need to get to you destination (no matter how far it is)