Question

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

Answer 1

Answer:

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 $V_1$, $x_1$, $t_1$ at the speed, distance and time that I code Heather

Let's call $V_2$, $x_2$, $t_2$ at the speed, distance and time Danielle codes.

Observe the following diagram:

(x) Heather <------ $x_1$ --------- hospital ---------- $x_2$ -----------> Danielle (-x)

So:

$V_1 = 35\ km/h$

$t_1 = 4\ h$

$V_2 = 50\ km/h$

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

That is to say:

$x_2 + x_1 = 290\ km/h$

We know that $x_1= v_1t_1$

$x_1 = 35(4)$

$x_1 = 140\ km$

We already know $x_1$, the distance from the hospital to Heather, so we can find $x_2$ and thus know $t_2$

So:

$x_2 = 290 - 140\\\\x_2 = 150\ km$

Then:

$t_2 = \frac{x_2}{v_2}\\\\t_2 = \frac{150}{50}\\\\t_2 = 3\ h$