SOLUTION: A trip between two cites 175 miles apart take 1.5 hrs less than by bus. The average speed of the bus is 15 miles per hour less than the train. Find the average speeds of the tra

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Question 522807: A trip between two cites 175 miles apart take 1.5 hrs less than by bus. The average speed of the bus is 15 miles per hour less than the train.
Find the average speeds of the train and the bus.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A trip between two cites 175 miles apart take 1.5 hrs less than by bus.
The average speed of the bus is 15 miles per hour less than the train.
Find the average speeds of the train and the bus.
:
Let s = speed of the bus
then
(s+15) = speed of the train
:
Write a time equation, time = dist/speed
:
Train time - Bus time = 1.5 hrs
175%2Fs - 175%2F%28%28s%2B15%29%29 = 1.5
;
multiply by s(s+15)
s(s+15)*175%2Fs - s(s+15)*175%2F%28%28s%2B15%29%29 = 1.5s(s+15)
:
Cancel out the denominators, results:
175(s+15) - 175s = 1.5s^2 + 22.5s
175s + 2625 - 175s = 1.5s^2 + 22.5s
:
a quadratic equation
0 = 1.5s^2 + 22.5s - 2625
get rid of the decimals, multiply by 2
3s^2 + 45s - 5250 = 0
You can use the quadratic formula here, but this will factor to:
(3s-105)(s+50) = 0
positive solution
3s = 105
s = 105/3
s = 35 mph is the speed of the bus,
then
35+15 = 50 mph is the speed of the train
:
:
Check this by finding the actual time of each
175/35 = 5.0 hrs
175/50 = 3.5 hrs
-----------------
differs: 1.5 hrs