SOLUTION: A car travels 40km per hour between two cities that are 90 km apart. How fast must the car travel on the return trip to average 50 km per hour for the round-trip?

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Question 203250: A car travels 40km per hour between two cities that are 90 km apart. How fast must the car travel on the return trip to average 50 km per hour for the round-trip?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A car travels 40km per hour between two cities that are 90 km apart.
How fast must the car travel on the return trip to average 50 km per hour,
for the round-trip?
:
Let s = speed required on the return trip to average 50 km/h
:
Write a time equation Time = dist%2Fspeed
:
outbound time + return time = time at 50 km/hr
90%2F40 + 90%2Fs = 180%2F50
Multiply by 200s:
200s*90%2F40%29 + 200s*90%2Fs = 200s*180%2F50
Cancel out the denominators:
5s(90) + 200(90) = 4s(180)
:
450s + 18000 = 720s
:
18000 = 720s - 450s
:
18000 = 270s
s = 18000%2F270
s = 662%2F3 km/hr required on the return trip
:
:
Check solution in the time equation
90%2F40 + 90%2F66.67 = 180%2F50
2.25 + 1.35 = 3.6