SOLUTION: Two cars leave an intersection at the same time. One is headed south at a constant speed of 40 miles per hour, the other is headed west at a constant speed of 30 miles per hour (se

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Question 1203928: Two cars leave an intersection at the same time. One is headed south at a constant speed of 40 miles per hour, the other is headed west at a constant speed of 30 miles per hour (see the figure). Express the distance d between the cars as a function of the time t. (Hint: At t = 0 the cars leave the intersection.)
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.

At the time t, the southern leg is 40t miles; the western leg is 30t.


The hypotenuse of the right angled triangle, which is the distance between the cars, is, according to Pythagoras

    d = sqrt%28%2840t%29%5E2+%2B+%2830t%29%5E2%29 = sqrt%281600t%5E2+%2B+900t%5E2%29 = sqrt%282500t%5E2%29 = 50t miles.


ANSWER.  The distance between the cars as function of the time is  d = 50t miles.

Solved.