I've been working on this for an hour and I know it's more simple than I'm making it. Please enlighten me.

Question

Cyclist 1 is traveling at 20 mph, Cyclist 2 is traveling at 14 mph. How long before they're 15 miles apart?

I've tried to fill in a block diagram and work from there, but, I end up with too many variables.

Answer 1

The key concept here is that the time they bike is the same for both.

I will assume they are traveling in opposite directions.

Let x miles be the distance the first one went, then 15-x is the distance the second one went
time of first = x/20
time for the second = (15-x)/14

solve x/20 = (15-x)/14

by cross-multiplying.

once you have x, put x into x/20 for the time in hours.

( I got .44 hours or 26.5 minutes.)

checking for reasonableness of answer.
26.5 minute is approx 1/2 hour
in 1/2 hour the first one went 10 miles in one direction, while the other biker went 7 miles, for a distance between of 17 miles.
since I estimated slightly over the time of the answer, I expected my estimated distance to be higher also.
So I am confident about my answer)

Answer 2

Thank you; however, the cyclists were traveling in the same direction, leaving at the same time. Therefore, I'm afraid I'm still without an answer.

Answer 3

bob columm covered the first 12 miles in 4 hours. he then increased the speed by 2 miles per hour. if the total distance of the trip was 52 miles, how long did it take to finish the trip?