A bus starts 30 minutes late and to reach its destination 150 km away on time, it increases its speed by 25 km/h. What is the usual speed of the bus?
Show answer & explanation
Correct answer: B
Explanation
Given:
Distance = 150 km
Bus is 30 minutes late
Speed increase = 25 km/h
Formula:
Time = Distance / Speed
Let the bus's usual speed = x km/h
Normal time = 150 / x
New speed = (x + 25) km/h
New time = 150 / (x + 25)
Time difference = 30 minutes = 1/2 hour
150/x − 150/(x + 25) = 1/2
150(x + 25) − 150x / x(x + 25) = 1/2
3750 / x(x + 25) = 1/2
x(x + 25) = 7500
x² + 25x − 7500 = 0
(x + 100)(x) − 75) = 0
x = 75 km/h