Question

A plane leaves St. Louis airport at 10:00am flying due north. Another plane from the same airport flies due south at 12:00pm. At 2:00pm, they are 1800 miles apart. Find the rate of each plane if the rate of the plane flying north is twice that of the plane flying south.

Answer 1

❗ ANSWER ❗

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

Hope it's helpful dear.......