Binomial Expansion?

[Ruby]

Hi, I have a problem that I think I know how to do, but I don't understand the teacher's "hint". Two opposing armies move towards each other with a relative speed of 1.5 mph. When they are 20 miles apart, a messenger whose running speed is 5 mph is sent from one army to the other. He continues to run back and forth at this speed with no rest untili the armies meet. How far does he run? (Remember: distance = rate*time. Also, look for binomial expressions in you analysis. Now, my thought is this: find how long it takes the two armies to meet. Then, see how far the messenger can go in that amount of time. Is that right? If so, what do binomial expansions have to do with anything?

 

[wjm11]

Two opposing armies move towards each other with a relative speed of 1.5 mph. When they are 20 miles apart, a messenger whose running speed is 5 mph is sent from one army to the other. He continues to run back and forth at this speed with no rest until the armies meet. How far does he run?

First find how long it takes the armies to meet:

t = d/r = (20 mi)/(1.5 mi/hr) = 13.33 hr

That is how long the runner is running. His distance traveled is:

D = rt

Can you finish?

 

[Ruby]

The messenger traveled 66.67 miles?