A car travelled at a speed of 45 km/h during the first part of its journey, and at a speed of 60 km/h for the rest of the journey. If the journey took 5 hours and the car covered 255 km in all, for how much time did it travel at 60 km/h?
Answers
Answer :-
Time taken to travel when car its speed is 60 km/h is 2 hours.
Solution :-
Total distance covered by a car = 255 km
Total time taken to cover the distance = 5 hours
Case 1
Speed of the car = 45 km/h
Let the distance covered be 'd' km and time taken to cover it be 't' hours
Speed = Distance/Time
⇒ 45 = d/t
⇒ 45t = d ---eq(1)
Case 2
Speed of the car = 60 km/h
Distance covered = Total distance - d = (255 - d) km
Time taken to cover the distance = Total time - t = (5 - t) hours
Speed = Distance/Time
⇒ 60 = (255 - d)/(5 - t)
⇒ 60(5 - t) = 255 - d
⇒ 300 - 60t = 255 - d
⇒ 300 - 255 + d = 60t
⇒ 45 + d = 60t
⇒ 60t = 45 + d---eq(2)
Divide eq(1) by eq(2)
⇒ 45t/60t = d/(45 + d)
⇒ 3/4 = d/(45 + d)
⇒ 3(45 + d) = 4d
⇒ 135 + 3d = 4d
⇒ 135 = 4d - 3d
⇒ 135 = d
⇒ d = 135
Substitute d = 135 in eq(1)
⇒ 45t = d
⇒ 45t = 135
⇒ t = 135/45
⇒ t = 3
Time taken to travel when car its speed is 60 km/h = (5 - t) = (5 - 3) = 2 hours.
Refer the given attachment
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