Two joggers set out at the same time from their homes 24 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 6 mph faster than the rate of other, find the rate of each.

Question

Two joggers set out at the same time from their homes 24 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 6 mph faster than the rate of other, find the rate of each. ​

Quizplus · Accepted Answer

Let's call the slower jogger's speed x. That means the faster jogger's speed is x + 6. We can use the formula distance = rate * time to create two equations:

First, we know that the two joggers are starting 24 miles apart and heading towards each other, so we can add their distances together to get 24 miles:

distance of jogger 1 + distance of jogger 2 = 24
xt + (x + 6)t = 24

We also know that they're going to meet somewhere in between their starting points in an hour and a half, or 1.5 hours:

t = 1.5

Now we can substitute that back into our first equation:

x(1.5) + (x + 6)(1.5) = 24

Simplifying that equation, we get:

1.5x + 1.5x + 9 = 24
3x = 15
x = 5

So the slower jogger is going 5 mph, and the faster jogger is going 5 + 6 = 11 mph. Therefore, the answer is C.

Two Joggers Set Out at the Same Time from Their