Question

A ship traveled for a total of 72 miles over the course of 6 hours. Heading south, the ship traveled at an average speed of 13 miles per hour, and heading east, it traveled at an average speed of 10 miles per hour. For how many hours was the ahi heading east?

Answer 1

Recall your d = rt, distance = rate * time

the rate going south is 13, the rate going east is 10

it took a total amount of 6hours and 72miles for the whole travel

so.. if going say hmmm South, it covered a distance of "d", then going East it covered a distance of the slack from 72 and "d", it covered "72 - d" miles

so, if going South it took "t" hours, then going East it took the slack from 6 and "t", or "6 - t" hours

thus      $\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ South&d&13&t\\ East&72-d&10&6-t \end{array} \\\\\\ \begin{cases} \boxed{d}=13t\\ 72-d=10(6-t)\\ ----------\\ 72-\boxed{13t}=10(6-t) \end{cases}$

solve for "t"

so, it travelled East for 6-t hours