Question

A car traveling 70 miles per hour is 20 miles behind a truck traveling 50 miles per hour. How long will it take the car to overtake the truck?

Answer 1

1 Hour

Explanation:

The car and truck are moving with uniform velocities.

• Let the velocity of car be `v_c`=70 miles/hr.

• Let the velocity of truck be `v_t`=50 miles/hr

Let the starting point of car be O then

The starting point of the truck will be 20 Miles from the point O.

Let us consider both car and truck are travelling in the straight line.

Before the car over taking the truck first it should equalise the distance travel by the truck

let us write it in a equation

1. distance travel by the car `S_c`= `v_c*t`
2. distance travel by the truck `S_t=v_t*t`

Where t is the time taken by the car to over take truck.

Here we doesn't include a think that initially with respect to O the
truck is at a distance of 20 Miles from the car.

Hence at time t the car overtake the truck(at that time distance from the point O is the same for both i.e, for the car and the truck)

we arrived at a relation,

`S_c=S_t+20`
`v_s*t=v_t*t+20`
Now giving the values to each terms we find the time taken by the car to overtake

`70*t=50*t+20`
#70*t-50*t=20 #
`20*t=20`
`t=1`

Hence the time taken by the car to overtake the truck is 1 hour

Answer 2

`1` hour

Explanation:

The car is travelling at a speed relative to the truck of `70" mph" - 50" mph"=20"mph"`
and therefore it will take the car `1` hour to travel the `20` miles between them.