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

Answer:

2.22

Step-by-step explanation:

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Answer 2

Answer:

They meet in 2.22 hours.

Step-by-step explanation:

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

$v_{R} = \frac{x_{R}}{t}$  

$x_{R} = v_{R}t$    (1)      

$v_{N} = \frac{x_{N}}{t}$  

$x_{N} = v_{N}t$   (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:

$x_{R} + x_{N} = v_{R}t + v_{N}t$

$t = \frac{x_{R} + x_{N}}{|v_{R}| + |v_{N}|} = \frac{40 mi}{8 mi/h + 10 mi/h} = 2.22 h$

Therefore, they meet in 2.22 hours.        

I hope it helps you!