SOLUTION: A can run 2 km in 4 min 20 seconds, while B can run this distance in 4 min 34 sec. By how much distance can A beat B?

Question 816679: A can run 2 km in 4 min 20 seconds, while B can run this distance in 4 min 34 sec. By how much distance can A beat B?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A runs 2 km in 4 minutes 20 seconds.
B runs 2 km in 4 minutes 34 seconds.
4 minutes 20 seconds is equivalent to 260 seconds.
4 minutes 34 seconds is equivalent to 274 seconds.
2 km is equal to 2000 meters.
the average speed of A is 2000 meters / 260 seconds which is equal to 7.692307692 meters per second.
the average speed of B is 2000 meters / 274 seconds which is equal to 7.299270073 meters per second.
in the time that A has run 2000 meters, B has run 7.299270073 meters per second times 260 seconds which means that B has run 1897.810219 meters.
this means that A has beat B by 2000 - 1897.810219 = 102.189781 meters.

the basic equation is rate * time = distance.
what you want to know in this problem is the rate that A and B each run at.
if rate * time = distance, then rate = distance / time.
what's what was determined above when i divided the distance that each ran by the time it took each to run it.
once you know the rate that each person runs at, then you can determine the distance that each runs at in the same amount of time.
since A was the faster person, you use the time that A used to run the 2000 meters and then figure out the distance that B ran in the same amount of time.

A runs 2000 meters in 260 seconds.
B runs 1897.810219 meters in 274 seconds.

you can also look at this as a ratio problem.
If B runs 2000 meters in 274 seconds, then how far has B run in 260 seconds.
your ratio would be:
2000 / 274 = x / 260
you would cross multiply to get 2000 * 260 = 274 * x
simplify that to get 520,000 = 274 * x
solve for x and you get x = 520,000 / 274 = 1897.810219 meters.
then you just take the difference between 2000 and 1897.810219 to get 102.189781.

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