Question

A car travels 25 km an hour faster than a bus for a journey of 500 km. The bus takes 10 hours more than the car.Find the speed of the car and the bus

Answer 1

Answer:

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

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

10xx - 12500 = 250x

10xx - 250x - 12500 = 0

the above quadratic equation is in standard form, with a=10, b=-250, and c=-12500

the quadratic has two real roots at:

x = 50

x = -25

x = speed of car = 50 kph

y = speed of bus = 25 kph