college algebra word problem

Question

Two planes leave from Atlanta, Georgia. One makes a 3.8

 hr flight to Seattle, Washington, and the other makes a 5

 hr flight to Boston, Massachusetts. The plane to Boston averages 44mph

 slower than the plane to Seattle. If the total distance traveled by both planes is 3124mi

, determine the average speed of each plane.

Answer 1

Let's call the Seattle flight plane 1 and the Boston flight plane 2

The time for the Seattle flight is 3.8 hours, so t₁ = 3.8

The time for the Boston flight is 5 hours, so t₂ = 5

We don't know the rate for either flight, so let's call the rate for the Seattle flight r₁

We do know that the Boston flight is 44 mph slower than the Seattle flight, so we can say r₂ = r₁ - 44

The total distance for both flights is 3124, so d₁ + d₂ = 3124

Since distance = rate * time, we can rewrite the distance equation in terms of rates and times:

d₁ + d₂ = 3124

r₁ * t₁ + r₂ * t₂ = 3124

Now we substitute the values for time we used above:

r₁ * 3.8 + r₂ * 5 = 3124

Now we substitute the value for r₂ in terms of r₁

3.8r₁ + 5(r₁ - 44) = 3124

3.8r₁ + 5r₁ - 220 = 3124

8.8r₁ = 3344

Now you can solve for r₁ and then solve for r₂