Question

Gretchen runs the first 4.0 km of a race at 5.0 m/s. Then a stiff wind comes up, so she runs the last 1.0 km at only 4.0 m/s.

Answer 1

Answer:

The velocity is $v = 4.76 \ m/s$

Explanation:

From the question we are told that

   The first distance is   $d_1 = 4.0 \ km = 4000 \ m$

   The  first speed  is  $v_1 = 5.0 \ m/s$

    The  second distance is  $d_2 = 1.0 \ km = 1000 \ m$

    The  second speed  is  $v_2 = 4.0 \ m/s$

Generally the time taken for first distance is  

      $t_1 = \frac{d_1 }{v_1 }$

        $t_1 = \frac{4000}{5}$

       $t_1 = 800 \ s$

The time taken for second  distance is

           $t_1 = \frac{d_2 }{v_2 }$

        $t_1 = \frac{1000}{4}$

       $t_1 = 250 \ s$

The total time is mathematically represented as

     $t = t_1 + t_2$

=>   $t = 800 + 250$

=>    $t = 1050 \ s$

Generally the constant velocity that would let her finish at the same time is mathematically represented as

      $v = \frac{d_1 + d_2}{t }$

=>    $v = \frac{4000 + 1000}{1050 }$

=>    $v = 4.76 \ m/s$