Question

A bus covers a certain distance with a uniform speeding the speed of the bus would have been increase by 15km/Hrithik’s would have taken 2hour less to cover same distrance and if the speed of the bus could have increase by 5km/Hr it would have taken one hour more to cover the same distance. Find the distance covered by the bus?

Answer 1

Let the distance covered by bus be xy.

Here x = speed and y = time

Distance = Speed × Time

A.T.Q

Case 1st

(x + 15) (y - 2) = xy

x (y - 2) [(+15) (y - 2)] = xy

xy - 2x + 15y - 30 = xy

- 2x + 15y = 30

2x - 15y = - 30 _____(1)

Case 2nd

(x - 5) (y + 1) = xy

x (y + 1) [(-5) (y + 1)] = xy

xy + x - 5y - 5 = xy

x - 5y - 5 = 0

x = 5 + 5y ____(2)

Put value of x in (1)

2 (5 + 5y) - 15y = - 30

10 + 10y - 15y = - 30

- 5y = - 30 - 10

- 5y = - 40

y = 8 ___(3)

Put value of y in (2)

x = 5 + 5 (8)

x = 5 + 40

x = 45 ___(4)

Distance = xy

= 45 × 8

$\boxed{\boxed{360 km}}$