The distance between two cities is ninety miles, and a woman drives from one city to the other at a rate of 45 mph. At what rate must she return if the total travel time is three hours and forty minutes?

Question

anonymous · Answer

the distance between the two cities is 90 miles
time = distance /speed
                                                                                                                                    90
so, while driving at the speed of 45 miles/h, time taken to cover 90 miles = ----- = 2h
                                                                                                                                     45

this means that the return trip has to be completed in 1 h 40 min = 100/60 h
and distance is still 90 miles
speed = distance/time
                    90                       60
speed = --------  = 90 x -----  = 5400/100 = 54 mph
                  100                       100
                  ----
                    60

so the speed of the return journey has to be 54 mph