Sam and Tom are competing in a swimming race being held over a number of laps of a pool. Sam is faster than Tom and is on his 2nd lap when, 10 meters from the far end of the pool, he passes Tom who is still on his 1st. lap. When Sam is on his 3rd lap and some 80 meters from the far end of the pool, he passes Tom nearing the end of his 2nd lap. Assuming that both swimmers swam at a constant speed and did not pause at any end, how long is the pool? Thanks.
+37084 I will assume a 'lap' is one length of the pool....
100m
Sam swims 110 m Tom has only swam 90 m
220 m Tom 180 m
If the pool is 100 Sam will be 80 meters from the end (on his 3rd lap) as will be Tom (but going opposite direction on his 2nd lap) and they are at the same times.
I'll work on entering here, how I derived it ...if you want it.
EP: I think you got it!. I will do it algeraically:
Let the length of the pool = L
2[L + 10] = [3L - 80], solve for L,
L = 100 meters.
+37084 Sam swims P +10 while
Tom swims P-10
Nex Sam has swimmed 3P-80 while
Tom has swimmed P+80 Where P = pool length
Since theyswim at a constant ratio:
(p+10)/(p-10) = (3p-80)/(p+80) cross multiply
p^2 + 80p +10p +800 = 3p^2 -30p -80p +800 simplify
p^2 +90p +800 = 3p^2 -110p +800
90p = 2p^2 -110p
0= 2p^2 -200p
0= p-100 or p=100m = pool length
