Question

By increasing her usual speed by 20 kilometers per hour, a bus driver decreases the time on a 20-kilometer trip by 5 minutes. How do you find the usual speed?

Answer 1

Usual speed of the bus was `60` km/hour.

Explanation:

Let the usual speed be `x` km/hour and the increased speed

is `(x+20)` km/hour. Time taken to cover `20` km trip at

`x` km/hour speed was `t_1= 20/x` hour and time taken to cover

`20` km trip at `(x+20)` km/hour speed was `t_2= 20/(x+20)`

By given condition `t_1-t_2=5/60=1/12` hour

`:.20/x - 20/(20+x)=1/12` . Multiplying by `12 x(x+20)` on both

sides we get, `240( 20+x) - 240 x= x(x+20)` or

`4800 + cancel(240 x) - cancel(240 x) = x^2+20 x` or

`x^2+20 x -4800 = 0 or x^2+80 x - 60 x- 4800 = 0` or

`x(x+80) -60 (x+80)=0 or (x+80)(x-60)=0 :.`

Either `x+80=0 :. x =-80 or x-60=0 :. x=60 ; x`

can not be negative `:.x=60` km .

Usual speed of the bus was `60` km/hour [Ans]