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?

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Answer 1 · 2018-04-21T11:25:26

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

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]