How Many Times Would Friends A & B Cross Each Other at the Track?

[zealot1985]

Two friends are at the local high school track, a circle measuring 440 yards for one complete lap. A can jog at 8.2 miles per hour while B’s jogging speed is 4.6 miles per hour. If they both start at the same point and jog in the same direction (say clockwise), how many times would they have crossed each other after a half hour? If they started off in opposite directions, what would your answer be?

 

[Rake-MC]

Find the faster runner's relative velocity to the slower runner (such that it appears the slower runner is stationary). Calculate how many laps he completes in half an hour, every full lap (440 yards) is every time he passes the other runner.

 

[zealot1985]

Runners going in the same direction:
8.2 - 4.6 = 3.6 * 0.5 => 1.8
1.8/0.25 = 7.2

Runners going in the opposite direction:
8.2 + 4.6 = 12.8 * 0.5 => 6.4
6.4/0.25 = 25.6

Is this correct you think?

 

[Rake-MC]

Hmm you might have to explain what you've done here a little. If it's to do with unit conversion, I can't help you a lot because in my country we use si units already.

I don't understand how you got in the first line: 8.2 - 4.6 = 3.6 * 0.5?
That sum is incorrect.

EDIT: I see what you've done now, it's very unorthodox and you could very well be marked down if it's assessed. However, it is correct provided that 440 yards is 1/4 of a mile.

 

[zealot1985]

This was abbreviated really, thank you for taking the time to look over this. I'll just write out the equations on a new line each time.
I do have another problem in another thread. Is it possible for you to take a look at that?