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?

1 Answer
Apr 21, 2018

Answer:

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]