Question

A ship traveled at an average rate of 22 miles per hour going east. It then traveled at an average rate of 17 miles per hour heading north. If the ship traveled a total of 212 miles in 11 hours, how many miles were traveled heading east?

Answer 1

recall your d = rt, distance = rate * time

let's say the ship went East at 22mph, now, the ship travelled a total of 212 miles in 11 hours... ok... how many miles did it go East? well, let's say it went "d" miles, and it took "t" hours.

now, if the ship after that went North at a rate of 17mph, then it took the slack from the 11 hours total and "d", or it took going North " 11 - t ", and it covered a distance, of also the slack from 212 miles and "d", or " 212 - d ".


`\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ East&d&22&t\\ North&212-d&17&11-t \end{array} \\\\\\ \begin{cases} \boxed{d}=22t\\ 212-d=17(11-t)\\ ----------\\ 212-\boxed{22t}=17(11-t) \end{cases}`

solve for "t", to see how long it took the ship going East.

how many miles it covered? well d = 22t