What is the average speed of each?

Question

Two planes are at different airports that are 555 miles apart. Both planes take off at noon one day and begin traveling towards each other.

The faster plane travels 10 miles per hour faster than the other plane.

What is the average speed of each plane if they reach each other after 1 ½ hours?

Answer 1

It's pretty nice to use the equation D = rt to solve this problem. D means distance, r means rate or speed, and t means time. I'm going to make a rough sketch of what's going on here. The planes are traveling towards each other like this.

 

A-------------><--------B

 

"A" and "B" represent the airports. The left arrow will represent the faster plane, which is traveling 10 miles per hour faster. We don't know the exact speed, but we do know that it's 10 more than the slower one. Therefore, the speed for the fast plane will be "r + 10" and the slow plane's speed will be just "r."

 

Let's make an equation for the fast plane. I'll use subscripts of "f" to mean fast. Also, both planes are traveling for one and a half hours. In other words, their traveling for 1.5 hours, so assign t = 1.5 for both planes.

 

D_f = r_ft_f

D_f = (r + 10)(1.5)

 

Now let's make the equation for the plane that's slow and takes its time.

 

D_s = (r)(1.5)

 

The weird part is to find the relationship between the two planes. Look at my lame sketch up above that represents the scenario. The two arrows represent the respective distances that both traveled. Because the two airports are 555 miles apart, the sum of their respective distances add up to 555.

 

D_f + D_s = 555

 

Substitute the equations for D_f and D_s into this.

 

D_f + D_s = 555

(r + 10)(1.5) + (r)(1.5) = 555

1.5r + 15 + 1.5r = 555

3r + 15 = 555

3r = 540

r = 180

 

Now we know r = 180. We assigned the speed of the slow plane to be a plain old r, so 180 miles per hour is the speed of the slow plane. The fast plane has a speed that's 10 more, so the fast plane's speed is 190. I hope this helps, and good luck with your math class!