The boat travels 60 miles to an island and the same 60 miles coming back. Changes in the wind and tide made the average speed on the return trip 3 mph slower than the speed on the way out. If the total time of the trip took 9 hours, find the speed going to the island and the speed on the return trip.

Answer 1

return speed = v - 3

time out = 60/v
time back = 60/(v-3)
so
60/v + 60/(v-3) = 9
60(v-3) + 60 v = 9 v(v-3)

9 v^2 -27v = 120 v - 180

9 v^2 - 147 v + 180 = 0
3 v^2 - 49 v + 60 = 0
(3 v -4)(v-15) = 0
v = 15 or v = 4/3
4/3 will not work because v - 3 is negative
try v = 15
15 and 15-3 = 12
then
60/v = 4
60/12 = 5
sure enough 9 hours