You can
put this solution on YOUR website! Jim can fill a pool carrying buckets of water in 30 minutes.
Sue can do the same job in 45 minutes. Tony can do the same
job in 1.5 hours. How quickly can all three fill the pool
together?
Let the answer be x minutes
>>...Jim can fill a pool...in 30 minutes...<<
Therefore in 1 minute Jim can fill 1/30 of the pool.
Therefore in x minutes Jim can fill x/30 of the pool.
>>...Sue can do the same job in 45 minutes...<<
Therefore in 1 minute Sue can fill 1/45 of the pool.
Therefore in x minutes Sue can fill x/45 of the pool.
>>...Tony can do the same job in 1.5 hours (90 minutes)...<<
Therefore in 1 minute Tony can fill 1/90 of the pool.
Therefore in x minutes Jim can fill x/90 of the pool.
With all three working together for x minutes they can
fill exactly ONE pool, so
Fraction of the pool Jim fills in those x minutes +
Fraction of the pool Sue fills in those x minutes +
Fraction of the pool Tony fills is those x minutes =
ONE whole pool filled.
So
x/30 + x/45 + x/90 = 1
Can you solve that? (Hint: multiply through by LCD = 90)
Answer x = 15 minutes
During those 15 minutes,
Jim fills 15/30 or 1/2 of the pool,
Sue fills 15/45 or 1/3 of the pool, and
Tony fills 15/90 or 1/6 of the pool.
Edwin
AnlytcPhil@aol.com
