Question

Two cars left the city for a suburb, 480 km away, at the same time. The speed of one of the cars was 20 km/hour greater than the speed of the other, and that is why it arrived at the suburb 2 hour earlier than the other car. Find the speeds of both cars.

Answer 1

Time taken by car A = 6 hr and time taken by car B is 8 hours

Step-by-step explanation:

Given:

Distance, d = 480 km

Let x be the time taken by B to reach the destination:

So,

Time taken by car A to reach the destination = x -2

We know:

Distance = speed X time

speed =
`(distance)/(time)`

On substituting the value we get:

Speed of car A =
`(480)/(x - 2)`

Speed of car B =
`(480)/(x)`

Since car A travelled 20 km/hr faster than the car B, the equation becomes:

`(480)/(x-2) = (480)/(x) + 20`

Multiplying both sides by (x - 2) we get:

`480 = (480(x-2))/(x)+ 20(x-2)\\ \\480 = (480x - 960)/(x) + 20x - 40\\\\480 = (480x - 960 + 20x^2 - 40x)/(x) \\\\480x = 20x^2 + 440x - 960\\\\20x^2 - 40x - 960 = 0\\\\x^2 - 2x - 48 = 0\\\\x = 8`

Therefore, time taken by car A = x - 2

= 8 - 2 hr

= 6 hr

Time taken by car B = 8 hr