Starting from 150 ft​ away, your friend skates toward you

Question

Starting from 150 ft​ away, your friend skates toward you and then passes you. She skates at a constant speed of 20​ft/s. Her distance d from you in feet after t seconds is given by d=|150-20t|. At what times is she 90ft from​ you?

Answer 1

Hello, Lizzie,

This is a slightly tricky problem unless you (and I) read the question carefully. The equation tells us the distance your friend is from you as a function of time. Let's check it out by calculating the time it takes her to reach you, the time it takes her to travel 150 feet. d, in this case, is 0 feet (she's arrived!).

Check it out by: 7.5 sec x 20ft/sec = 150 feet. So that works.

Now let's answer the question "At what times is she 90ft from​ you?" Note "times" is plural and the problem states ". . .passes you." So there would be two times your friend is 90 feet from you. How do we find those times?

The first is easy. Just use the equation and solve:

The time it takes to go 90 feet past you is the next question. Here's the tricky part. The equation is still valid, but it uses your location as the "0" point. So when she goes by, she is, mathematically, going in a negative direction. So let's try using a negative 90 feet in the equation:

In summary:

I hope this helps,

Bob

Answer 2

Since you have a target distance of 90ft then set d =90. Thus 90=|150-20t|. From here, solve the two equations 90=150-20t and -90=150-20t.

Thus the answers are t=3sec and t=12sec