Question

Reagan and Nathan are 40 miles apart on a bike trail when they start pedaling toward each other on their b bicycles. Reagan rides at a constant speed of 8 miles per hour, and Nathan rides a constant speed of 10 miles per hour. How long does it take until Reagan and Nathan meet?

Answer 1

2.22

Explanation:

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Answer 2

They meet in 2.22 hours.

Explanation:

We can find the time at which Reagan and Nathan meet by equaling the time as follows:

`v_(R) = (x_(R))/(t)`

`x_(R) = v_(R)t` (1)

`v_(N) = (x_(N))/(t)`

`x_(N) = v_(N)t` (2)

Where R is for Reagan and N for Nathan.

Knowing that:

`x_(R) + x_(N) = 40 mi`

By adding equations (1) and (2) we have:

`x_(R) + x_(N) = v_(R)t + v_(N)t`

`t = (x_(R) + x_(N))/(|v_(R)| + |v_(N)|) = (40 mi)/(8 mi/h + 10 mi/h) = 2.22 h`

Therefore, they meet in 2.22 hours.

I hope it helps you!