Problema Solution
On a road trip you are taking you decide to go over a fairly large hill. The hill is two miles long, one mile up, one mile down. If your car averaged 30 miles per hour on the way up, how fast will you have to go down the hill in order to average 60 miles per hour over the entire hill?
Answer provided by our tutors
let
d = 2 mi the total distance
v1 = 30 mph the average speed up
v2 = the average speed down
v = 60 mph the average speed over the entire hill
the average speed = the total distance/the time of the travel
the time up is: 1/v1 = 1/30 hr
the time down is: 1/v2 hr
the total time of the trip is: t = 1/30 + 1/v2
v = d/t
v = 2/(1/30 + 1/v2)
2/(1/30 + 1/v2) = 60 divide both sides by 3
1/30 + 1/v2 = 2/60
1/30 + 1/v2 = 1/30
1/v2 = 0
the above equation has no solution thus the problem has no solution.