Question

Valerie is taking a road trip over spring break. At 4:30 p.m. she looks down at her speedometer and notices that she is going 45 mph. Ten minutes later she looks down at the speedometer again and notices that she is going 55 mph. When was she moving exactly 50 mph?Select one:a. 4:30 p.m.b. 4:35 p.m.c. 4:40 p.m.d. Cannot be determined

Answer 1

b. 4:35 p.m

Explanation:

Her speed in t minutes after 4:30 p.m. is modeled by the following equation:

`v(t) = v(0) + at`

In which v(0) is her speed at 4:30 pm and a is the acceleration.

At 4:30 p.m. she looks down at her speedometer and notices that she is going 45 mph.

This means that
`v(0) = 45`

Ten minutes later she looks down at the speedometer again and notices that she is going 55 mph.

This means that
`v(10) = 55`

So

`v(t) = v(0) + at`

`55 = 45 + 10a`

`10a = 10`

`a = 1`

So

`v(t) = 45 + t`

When was she moving exactly 50 mph?

This is t minutes after 4:30 p.m.

t is found when v(t) = 50. So

`v(t) = 45 + t`

`50 = 45 + t`

`t = 5`

5 minutes after 4:30 p.m. is 4:35 p.m.

So the correct answer is:

b. 4:35 p.m