Question

Gabby,a college student,headed home for thaksgiving.He rode his bike at a speed of 18 miles per hour to the town where his two sisters,Ariella and Rachelle,live. They all got in Ariellas car and drove to their patents home. On the car trip,the siblings averaged 60 miles per hour. The total distance from Gabbys house to their parents house (via his sisters house) is 435 miles,and Gabby traveled for 9 hours. How far is it from Gabbys house to his sisterss house?

Answer 1

Answer:

The distance is  $S_1 = 45 \ miles$

Step-by-step explanation:

From the question we are told that

   The speed at which Gabby rode his bike is  $v = 18 \ miles / hour$

   The average speed of the car is  $u = 60 \ miles / hours$

   The distance from Gabby's house to the parents house is  $d = 435 \ miles$

   The time taken for Gabby to get to his parents house is  t =  9 hours

Generally the distance from Gabby's house to his parent house is mathematically reparented as

        $S_1 + S_2 = d$

Here $S_1$ is the distance from Gabby's house to his sisters house which is mathematically represented as

     $S_1 = t_1 * v$

=> Here $t_1$ is the time taken to move from Gabby's house to his sisters house

while  $S_2$ is the distance from his sisters  house to his parents house which is mathematically represented as

      $S_2 = t_2 * u$

So

      $vt_1 + ut_2 = d$

=>  $18t_1 + 60t_2 = 435 --- (1)$

Generally the total time taken to arrive his parents house from his house is mathematically represented as

        $t_1 + t_2 = t$

=>    $t_1 + t_2 = 9 --- (2)$

Solving equation 1 and 2  simultaneously we have that

        $18t_1 + 60t_2 = 435 --- (1)$

         $t_1 + t_2 = 9 --- (2)$

multiply equation 2 by 18  and equation 1 by 1

          $18t_1 + 60t_2 = 435 --- (3)$

         $18t_1 +18 t_2 = 162 --- (4)$

Substracting equation 3 from 4

          $0t_1 + 42t_2 = 273$

=>     $t_2 = \frac{273}{42}$

=>     $t_2 = 6.5 \ hours$

substituting $t_2$ into equation 2

       $t_1 + 6.5 = 9 --- (2)$

=>     $t_1 = 2.5 \ hours$

So the distance  from Gabby's house to his sisters house is mathematically represented as

          $S_1 =2.5 * 18$

=>        $S_1 = 45 \ miles$