Jimmy travels from Point A to Point B at a speed of 40 mph, then using the same road, Jimmy travels from Point B to Point A at a speed of 60 mph.
What is the average speed for the round trip?
Why is the answer not 50?
Let the distance from A to B be L miles
time from A to B: t1 = L/40 hours
time from B to A: t2 = L/60 hours
Average speed for round trip = total distance/total time
so average speed = 2L/(t1 + t2) = 2L/(L/40 + L/60) = 2/(1/40 + 1/60) = 48 mph
You have to take into account the TIME at each speed.....the TIME to travel the same distance will be LONGER for 40 m/hr vs 60 m/hr so the AVERAGE will be weighted more toward the 40 m/hr ...
40 x t1 = d d/40 = t1
60 x t2 = d d/60 = t2
2d/avg = t1 + t2 = d/40 + d/60
2d/avg = (3d+2d)/120
2/avg = 5/120
avg/2 = 120/5
avg = 240/5 = 48 m/hr