A pool can be filled by one pipe in 20 hours and by a second pipe in
60 hours. How long will it take using both pipes to fill the pool?
Make the chart below. It is just like a D=RT chart except that
D stands for "DEEDS" not "DISTANCE". In other words, D stands
for the number of DEEDS or JOBS or pools filled in each case.
I'll use "JOBS".
No of jobs Rate in jobs per hour Time in hours
1st pipe only
2nd pipe only
Both pipes
------------------------
We read:
>>...A pool can be filled by one pipe in 20 hours...<<
So that's 1 job in 20 hours. So we fill in 1 for the number
of jobs which pipe 1 alone does and 20 for the number of hours.
No of jobs Rate in jobs per hour Time in hours
1st pipe only 1 20
2nd pipe only
Both pipes
-------------
Next we read:
>>...A pool can be filled...by a second pipe in 60 hours...<<
That's 1 job in 60 hours for the 2nd pipe. So we fill in 1 for the number
of jobs which the 2nd pipe does and 60 for the number of hours.
No of jobs Rate in jobs per hour Time in hours
1st pipe only 1 20
2nd pipe only 1 60
Both pipes
-----------------------
Now we read the question:
>>...How long will it take using both pipes to fill the pool...<<
That asks how many hour would it that both pipes to do 1 job. So we
let x be the number of hours it would take them to do 1 job, working
together. So we efill in 1 for the number of jobs and x for the
number of hours.
No of jobs Rate in jobs per hour Time in hours
1st pipe only 1 20
2nd pipe only 1 60
Both presses 1 x
----------------------
Now we fill in the rates by using the equivalent of
DISTANCE
RATE = ----------
TIME
which is:
NUMBER of JOBS
RATE = -----------------
TIME
No of jobs Rate in jobs per hour Time in hours
1st pipe only 1 20
2nd pipe only 1 60
Both presses 1 x
Now we use the formula:
Rate of 1st pipe + Rate of 2nd pipe = Rate of both pipes together
+ =
Can you solve that? You have to multiply through by the
LCD of 60x. If you can't solve it post again asking how.
Answer: 15 hours.
Edwin