Thread: Race word problem

At a recent world cup 10000m speed skating race, the winner, A, finished in 13 minutes 20.4 seconds. The last place finisher, B, took 15 minutes 37.0 seconds. The track is 400 m long.
i. How many meters did B still have to run when A finished?
ii. How far had A run when he first overlapped B?
iii. How many times was B lapped?

10000m/400m= 25 laps
A= 800.4 seconds/25 laps = 32.016 seconds/lap
B=937 seconds/25 laps = 37.48 seconds /lap

i. 37.48seconds/1lap=800.4seconds/x
x=8542.2
B had 8542.2 meters done when A finished, so B had 10000-8542.2=1457.8 left to go.

I would like help on parts ii & iii because I am not sure how to set up the equation where A's distance =B's distance. nor can I figure out how to tell how many times B was lapped.
My guess is that you set the velocity and time of A equal to the velocity of b and solve for the time but I'm not sure.

The first part is okay.

ii. How far had A run when he first overlapped B?
Rate of A = 10,000 /800.4 = 12.49375 m/sec
Rate of B = 10,000 /937 = 10.67236 m/sec

A had run 1 more lap than B when he overtook B, so,
12.49375(t) = 10.67236(t) +400
t = 400 /(12.49375 -10.67236) = 219.61249 sec.
Hence, A ran
(12.49375 m/sec)(219.61249 sec) = 2743.78 meters -------answer.
... when he caught up with B for the first time

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iii. How many times was B lapped?

From part (ii) above, A overlapped B every 2743.78 meters, so,
10,000 /2743.78 = 3.6446
Meaning, A overlapped B, 3 times --------------answer.

thank you very much. I wish I would have got that myself.