Question

A car travels 25 km an hour faster than a bus for a journey of 500 km. if the bus takes 10 hours more than the car, then the speeds of the car and the bus are

Answer 1

x = speed of car
y = speed of bus

x = y + 25

s = d/t
t = d/s

time of car:
a = 500/x

time of bus:
b = 500/x + 10

speed of the car:
s = d/t
x = y + 25-----(i)

d/a = d/b + 25
500/a = 500/b + 25
500/(500/x) = 500/(500/x + 10) + 25

x = 500/(500/x + 10) + 25
x - 25 = 500/(500/x + 10)
(x - 25)(500/x + 10) = 500

500 + 10x - 12500/x - 250 = 500
10x - 12500/x = 250
10x^2 - 12500 = 250x
x^ - 25x - 1250 = 0

so x^2 -50x + 25x - 1250 = 0
     x(x-50) + 25(x-50) =0
    (x-50) (x+25) =0
so x = 50 
and by (i) equation

x = speed of car = 50 km/hr
y = speed of bus = 25 km/hr

i hope it will help you
regards

Answer 2

Answer:

Step-by-step explanation:

a car travel (distance)=25 km in 1 hour

(speed)=distance/time

25km/1h = 25km/h

The Bus travel (distance) = 500km in 10 hour

(speed)=distance/time

500km/10h = 50km/h

===>(25 and 50)km/h