Heather left the hospital and drove toward the desert at an average speed of 35 km/h. danielle left sometime later driving in the opposite direction with an average speed of 50 km/h. after heather had driven for four hours they were 290 km apart. how long did danielle drive

Danielle drove 3 hours

Step-by-step explanation:

Suppose Heather moved in the x direction.

Then Danielle moved in the opposite direction, that is, she moved in the -x direction.

Let's call , , at the speed, distance and time that I code Heather

Let's call , , at the speed, distance and time Danielle codes.

Observe the following diagram:

(x) Heather <------ --------- hospital ---------- -----------> Danielle (-x)

So:

We know that after 4 hours the distance between Heather and Danielle was 290 km.

That is to say:

We know that

We already know , the distance from the hospital to Heather, so we can find and thus know

So:

Then:

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.