A bus left 40 minutes late due to bad weather and order to reach its destination 16 km away in time, it had increase its speed by 4 kmph from its usual speed. Find the usual speed of the bus?

Question: A bus left 40 minutes late due to bad weather and order to reach its destination 16 km away in time, it had increase its speed by 4 kmph from its usual speed. Find the usual speed of the bus?

Solution:
Let
usual speed be x kmph,
then new speed will be (x + 4) kmph.

∴ Time taken to cover 16 km with speed x kmph = 16/x

∴ Time taken to cover 16 km with Speed (x + 4) kmph = 16/(x + 4)

ATQ,
(16/x) - {16/(x + 4)} = 40 min
⇒ {16(x + 4) - 16x}/x(x + 4) = 40/60
⇒ (16x + 64 - 16x)/x(x + 4) = 2/3
⇒ 64/(x² + 4x) = 2/3
⇒ 2(x² + 4x) = 192
⇒ x² + 4x = 96
⇒ x² + 4x - 96 = 0
⇒ x² + 12x - 8x - 96 = 0
⇒ x(x + 12) - 8(x +12) = 0
⇒ (x + 12)(x - 8) = 0
∴ x = -12 or 8
[But, speed cannot be negative]

So usual speed will be 8 km/h