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

Answer:

The  time taken is  $t = 32.5 \ s$

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

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

   $t = 32.5 \ s$