A bus covers a certain distance with uniform speed. If the speed of the bus would have been increased by 15kmph, it would have taken two hours less to cover the same distance. And if the speed of the bus would have been decreased by 5kmph ,it would have taken one hour more to cover the same distance. Find the distance covered by the bus.
Answers
Let say Say Distance Covered by Bus = D km
Speed of Bus = S km/hr
Time to be taken = D/S hr
if the speed of the bus would have been increased by 15 km/h, it would have taken two hours less to cover the same distance
=> D/(S + 15) = D/S - 2
=> DS = DS + 15D - 2S² - 30S
=> 2S² + 30S = 15D
if the speed of the bus wolud have decreased by 5 km/h,it would have taken one hour more to cover the same distance.
=> D/(S - 5) = D/S + 1
=> DS = DS - 5D + S² - 5S
=> S² - 5S = 5D
=> 3S² - 15S = 15D
2S² + 30S = 3S² - 15S
=>S² = 45S
=> S = 45
Speed of Bus = 45 km/hr
S² - 5S = 5D
=> 45² - 5*45 = 5D
=> D = 360
the distance covered by the bus = 360 km
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