Problema Solution
Fritz normally commutes at an average speed of 40 miles per hour, but this morning's heavy traffic held him to only 30 miles per hour. He must determine whether he can drive home fast enough this evening to maitain his usual round-trip average speed.
Answer provided by our tutors
let
v1 = 40 mph
t = the time he usually travels
v2 = 30 mph
t1 = the time he drives with 30 mph
t2 = the rest of the time
v = the new speed to maintain his usual round-trip average speed
average speed = distance/time
d = 40t
first he drives t1 hours with 30 mph that is a distance of 30t1
then he drives t2 hours with a new speed v that is a distance of t2*v
30t1 + t2*v = 40*t
solve by v
v = (40t - 30t1)/t2
the rest of the trip he needs to drive with speed v = (40t - 30t1)/t2 to maintain his usual round-trip average speed.