Question 156603This question is from textbook
: A train travelled at m mi at a speed of s mph. A bus followed the same rout travelled 5 mph slower. How much longer did the bus take than the train to make this trip? Write the answer as a singla rational expression.
This question is from textbook
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! A train travelled at m mi at a speed of s mph. A bus followed the same rout travelled 5 mph slower. How much longer did the bus take than the train to make this trip?
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Apply the "distance formula"...
d = rt
where
d is distance
r is rate or speed
t is time
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From the problem we get the following info:
speed of train is 's' mph.
speed of bus is 's-5' mph.
distance traveled is 'm'.
.
plugging in what we know about the bus using the distance formula:
m = (s-5)t
t = m/(s-5)
therefore, "time for bus to travel distance" is m/(s-5)
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plugging in what we know about the bus using the distance formula:
m = (s)t
t = m/s
therefore, "time for train to travel distance" is m/s
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"additional time it took for bus" = "time for bus to travel distance" - "time for train to travel distance"
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"additional time it took for bus" = m/(s-5) - m/s
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Solution: m/(s-5) - m/s
Or, factoring out the 'm':
m(1/(s-5) - 1/s)
or,
m((s/(s^2-5s) - (s-5)/(s^2-5s))
m((s - (s-5))/(s^2-5s)
m(s - s + 5)/(s^2-5s)
m(5/(s^2-5s))
(5m)/(s^2-5s)
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