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A plane leaves St. Louis airport at 10:00a.m. flying due north. Another plane from the same airport flies due south at 12:00p.m. At 2:00p.m. they are 1,800 miles apart. Find the rate of each plane if the rate of the plane flying north is twice that of the plane flying south.

Respuesta :

calculista

Let

x---------> the rate of the plane flying north

y--------> the rate of the plane flying south

we know that

x=2y-----> y=(x/2)---------> equation 1

rate=distance/time

1) Find the distance at 2:00p.m------> plane flying north

2:00p.m-10:00a.m--------> 14:00-10:00=4 hours

distance 1=rate*time------> distance 1=x*4

2) Find the distance at 2:00p.m------> plane flying south

2:00p.m-12:00p.m--------> 14:00-12:00=2 hours

distance=rate*time------> distance 2=y*2

substitute equation 1 in the formula above

distance2=(x/2)*2-----> distance2=x

we know that

distance 1+distance 2=1,800 miles

so

4x+x=1,800------> 5x=1,800-------> divide by 5 both sides

x=360 miles/hour

y=360/2------> y=180 miles hour

therefore

the answer is

the rate of the plane flying north is 360 miles/hour

the rate of the plane flying south is 180 miles hour

Rate of plane flying north is 360 miles/hour.

Rate of plane flying south is 180 miles/hour.

Step-by-step explanation:

Given :

Let 'a' be the rate of plane flying north and 'b' be the rate of plane flying south.

a = 2b ---- (1)  (given)

Calculation :

We know that

[tex]\rm rate = \dfrac{distance}{time}[/tex]

So time taken by both the plane to flying 1800 miles apart is 4 hours and 2 hours respectively.

Therefore,

[tex]\rm d_1 = 4a[/tex] ---- (2)

[tex]d_2= 2b[/tex] ----- (3)

[tex]d_1 +d_2=1800[/tex] ----- (4)  (Given)

From equation (2), (3) and (4)

[tex]4a +2b = 1800[/tex] ---- (5)

From equation (1) and (5)

[tex]8b +2b = 1800[/tex]

[tex]\rm b = 180 \; miles/hour[/tex]

From equation (1) we get

a = 360 miles/hour

Rate of plane flying north is 360 miles/hour.

Rate of plane flying south is 180 miles/hour.

For more information, refer the link given below

https://brainly.com/question/18667145?referrer=searchResults

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