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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

Respuesta :

carlosego

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 [tex]V_1[/tex], [tex]x_1[/tex], [tex]t_1[/tex] at the speed, distance and time that I code Heather

Let's call [tex]V_2[/tex], [tex]x_2[/tex], [tex]t_2[/tex] at the speed, distance and time Danielle codes.

Observe the following diagram:

(x) Heather <------ [tex]x_1[/tex] --------- hospital ---------- [tex]x_2[/tex] -----------> Danielle (-x)

So:

[tex]V_1 = 35\ km/h[/tex]

[tex]t_1 = 4\ h[/tex]

[tex]V_2 = 50\ km/h[/tex]

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

That is to say:

[tex]x_2 + x_1 = 290\ km/h[/tex]

We know that [tex]x_1= v_1t_1[/tex]

[tex]x_1 = 35(4)[/tex]

[tex]x_1 = 140\ km[/tex]

We already know [tex]x_1[/tex], the distance from the hospital to Heather, so we can find [tex]x_2[/tex] and thus know [tex]t_2[/tex]

So:

[tex]x_2 = 290 - 140\\\\x_2 = 150\ km[/tex]

Then:

[tex]t_2 = \frac{x_2}{v_2}\\\\t_2 = \frac{150}{50}\\\\t_2 = 3\ h[/tex]

SaniShahbaz

Answer:

Danielle travelled for 3 hours

Distance travelled by Danielle: 150km

Step-by-step explanation:

We are asked to find out the time that Danielle travelled and the distance travelled by her.

Average Speed of Heather, v = 35 km/hr

Time that Heather travelled, t = 4hr

Distance travelled by Heather, s(heather) = v * t = 35 * 4 = 140 km

Now we are also given the total distance travelled by them which is 290 km

Total Distance, s(total) = 290km

Distance travelled by Danielle would be equal to Total distance minus Distane travelled by Heather

s(Danielle) = s(total) - s(heather)

                  = 290 - 140 = 150 km

Time travelled by Danielle would be calculated then:

Speed of Danielle = 50 km/hr

t = [tex]\frac{s}{v} = \frac{150}{50} = 3 hrs[/tex]

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