Applications of Linear Equations. 9th grade math homework

Question

Two planes left the same airport at the same time traveling in opposite directions. The first plane traveled at an average rate of 30 mph slower than the second plane. After 3 hours, the planes were 3150 miles apart.

Enter an equation that can be used to determine when the planes are 3150 miles apart, where x represents the average rate of the second plane.

Enter the average rate of change of the slower plane.

Answer 1

y = first plane; x = second plane.

 

Here's what we know:

Distance = rate * time

3150 mi/hr / 3 hours = 1050 miles

So after 1 hour, the planes will be 1050 miles apart.

(Also mph equates to ^mi/_hr)

 

1050 miles = x * 1hour + y * 1hour

y = x - 30 mph

 

1050 miles = (x + y)1hour

1050 ^mi/_hr = x + (x - 30)

1050 ^mi/_hr = 2x - 30

1080 ^mi/_hr = 2x

540 ^mi/_hr = x

 

y = (540 - 30) mph

y = 510 mph

 

Check:

3150 miles = (540 mph + 510 mph)3 hours

3150 miles = 1050 mph * 3 hours

3150 miles = 3150 miles