Question

In his​ motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing​ spot, a distance of 264 ​mi, in 6 hr.​ Returning, he finds that the trip​ downstream, still at top​ speed, takes only 5.5 hr. Find the rate of​ Bill's boat and the speed of the current. Let x​ = the rate of the boat in still water and y​ = the rate of the current.

Answer 1

Answer:

The values are   $x = 46 miles /hr$

                            $y = 4 \ miles / hr$

Step-by-step explanation:

From the question we are told that

   The distance covered is  d =  264 miles

     The time taken is $t_1 = 6 hours$

     The time taken for the return trip is  $t_2 = 5.5 \ hours$

Generally during the trip  toward fishing spot , the velocity is mathematically represented as

     $v_t = \frac{d}{t_1 } = x - y$

=>  $v_t = \frac{264}{6 } = x - y$

=>    $x - y = 44 \cdots 1$

Generally during the  return trip  , the velocity is mathematically represented as

      $v_r = \frac{d}{t_2} = x+ y$

=>   $v_r = \frac{264}{5.5} = x+ y$

=>   $48 = x+ y\cdots 2$

add equation 1 and 2

       $2x = 92$

=>    $x = 46 miles /hr$

substituting this  into  equation 1

     $46 - y = 44 \cdots 1$

=>   $y = 4 \ miles / hr$