Before solving the problem I just want to give you the heads

Before, solving the problem, I just want to give you the heads up. It\'s Application of Rational Equations. I can\'t find the specific title to relate with my story problems. My chapter in the book is Chapter Six Solving Rational Equations and Application of rational Equations. Hope it helps! (D=RxT)
*A twin engine plane can fly 800 miles in the same amount of time that it takes a single engine plane to fly 600 miles. The rate of the twin engine plane is 50 mph faster than that of the single engine plane. Find the rate of each plane.

Solution

Given: D = R x T

where D - Distance; R - Rate;   T - Time taken.

Let Rate of twin engine plane be Rt and single engine plane be Rs.

Condition 1:

Time taken by twin plane for travelling 800 miles = Time taken by single plane for travelling 600 miles.

Time = Distance/ Rate

So, 800/ Rt = 600 / Rs

On Cross multiplying, we get: 800 Rs = 600 Rt

Divide by 200 both sides, we get: 4Rs = 3Rt                   - Equation 1

Condition 2:

Rate of twin engine plane is 50 mph faster than that of single engine plane.

Rt = 500 + Rs - Equation 2.

Plugin value of Rt from Equation 2, in Equation 1.

4Rs = 3Rt

4Rs = 3(500 + Rs)

4Rs = 1500 + 3Rs

-3Rs -3Rs

Rs = 1500              

4Rs = 3Rt

4* 1500 = 3Rt

Rt = 2000

Hence, Rate of Twin engine plane = 2000mph , and single engine plane = 1500 mph