Math Problem-Flying

Question

Flying against the wind, a jet travels 6660mi in 9 hours. Flying with the wind, the same jet travels 4900mi in 5 hours. What is the rate of the jet in still air and what is the rate of the wind?

Answer 1

Let w be the speed of the wind, and j the speed of the jet in still air. The trick to solving this one is to write expressions for the speed of the jet with the wind and against the wind. When it's flying against the wind, the ground speed is j minus the speed of the wind: j-w. Flying down wind, the wind adds to its speed, so we have j+w. We can use these two expressions to write equations for the two situations described in the problem.

Against the wind, it flew 6660 miles in 9 hours, or 6660 miles per 9 hours. Its speed was (j-w) = 6660/9 miles/hour. Notice how the units miles and hours can be used to tell you how to write that equation. "Per" means "divided by".

With the wind its speed was 4900 miles per 5 hours. (j+w) = 4900/5 miles / hour.

We have two independent equations with two unknown variables (j and w), so we should be able to solve the system of equations.

j-w = 6660/9

j+w= 4900/5

We can simplify the fractions since 6660 is evenly divisible by 9 and 4900 by 5.

This will simplify things later.

j-w = 740

j+w = 980

Add these two equations:

2j +w-w =1720

2j = 1720

j = 860

Now we can substitute 860 for j in either of the original equations to find w.

j+w = 980

860+w = 980

w = 980-860

w = 120

Check:

j-w = 6660/9

860-120 =? 740

740 = 740

j+w= 4900/5

860+120 =? 980

980 = 980