A train travelled at m mi at a speed of s mph A bus followed

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.

Solution

Apply the \"distance formula\"...
d = rt
where
d is distance
r is rate or speed
t is time
.
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)
.
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
.
\"additional time it took for bus\" = \"time for bus to travel distance\" - \"time for train to travel distance\"
.
\"additional time it took for bus\" = m/(s-5) - m/s
.
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)