Landon can climb a certain hill at a rate that is 3.5 mph slower than his rate coming down the hill. If it take him 4 hours to climb the hill and 135 minutes to come down the hill. what is his rate coming down.

Answer 1

coming down rate --- x mph
going up rate -----< x-3.5

time going up = hill/(x - 3.5)
hill/(x - 3.5) = 4
hill = 4(x - 3.5)

time going down = hill/x
hill/x = 135/60 = 9/4
hill = (9/4)x

4(x - 3.5) = (9/4)x
16(x-3.5) = 9x
16x - 56 = 9x
7x = 56
x = 8

rate going down is 8 mph
(rate going up is 4.5 mph)

check:
length of hill = (9/4)(8) = 18 miles

time to come down = 18/8 = 2.25 hrs = 135 minutes
time to go up = 18/(8-3.5) = 4 hrs
checks out!