A train travels 180 km at a uniform speed. If the speed had been 15 km/h more, it would have taken 1 hour less to cover the same distance.
What is the original speed of the train?
Show answer & explanation
Correct answer: B
Explanation
Distance = 180 km
Time decreases by 1 hour when speed increases.
Let the original speed = x km/h
Original time = 180/x
New speed = x + 15
New time = 180/(x + 15)
180/x − 180/(x + 15) = 1
[180(x + 15) − 180x] / [x(x + 15)] = 1
2700 / [x(x + 15)] = 1
x² + 15x = 2700
x² + 15x − 2700 = 0
(x − 45)(x + 60) = 0
x = 45 km/h