Question

How long does it take an automobile traveling 66.7 km/h to become even with a car that is traveling in another lane at 52.7 km/h if the cars' front bumpers are initially 119 m apart?

Answer 1

The time taken is
`t = 32.5 \ s`

Step-by-step explanation:

From the question we are told that

The speed of first car is
`v_1 = 66.7 \ km/h = 18.3 \ m/s`

The speed of second car is
`v_2 = 52.7 \ km/h = 14.64 \ m/s`

The initial distance of separation is
`d = 119 \ m`

The distance covered by first car is mathematically represented as

`d_t = d_i + d_f`

Here
`d_i` is the initial distance which is 0 m/s

and
`d_f` is the final distance covered which is evaluated as
`d_f = v_1 * t`

So

`d_t = 0 \ m/s + (v_1 * t )`

`d_t = 0 \ m/s + (18.3 * t )`

The distance covered by second car is mathematically represented as

`d_t = d_i + d_f`

Here
`d_i` is the initial distance which is 119 m

and
`d_f` is the final distance covered which is evaluated as
`d_f = v_2* t`

`d_t = 119 + 14.64 * t`

Given that the two car are now in the same position we have that

`119 + 14.64 * t = 0 + (18.3 * t )`

`t = 32.5 \ s`