Aplane 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.

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

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

Therefore,

---- (2)

----- (3)

----- (4)  (Given)

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

---- (5)

From equation (1) and (5)

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.

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