I have tried repeatedly to figure these problems. I have 28 problems so I am getting help with 6. Thank you so much for all your help!!!
One pipe can fill a tank in 40 minutes and a larger pipe can fill it in 25 minutes. After the smaller pipe has been operating for 30 minutes the larger pipe is also turned on. How many more minutes does it take to fill the tank?
Make this chart, filling in the known quantities and let the unknown
time for the number of minutes more for both pipes to fill the tank
be t:
number of
tanks or parts rate in
of tanks per time in
tanks filled minute minutes
small pipe in general 1 40
large pipe in general 1 25
small pipe alone 30
both pipes together t
Now find the two rates by dividing the number of tanks filled, which
is 1, in the general case by the time to get their rates in tanks per
minute:
number of
tanks or parts rate in
of tanks per time in
tanks filled minute minutes
small pipe in general 1 1/40 40
large pipe in general 1 1/25 25
small pipe alone 30
both pipes together t
Now fill in the rate for the small pipe alone for the 30 minutes also
as 1/40:
number of
tanks or parts rate in
of tanks per time in
tanks filled minute minutes
small pipe in general 1 1/40 40
large pipe in general 1 1/25 25
small pipe alone 1/40 30
both pipes together t
Now fill in the part of the tank filled by the smal pipe alone
for the 30 minutes by multiplying the rate by the time,
getting 30/40 or 3/4 of a tank:
number of
tanks or parts rate in
of tanks per time in
tanks filled minute minutes
small pipe in general 1 1/40 40
large pipe in general 1 1/25 25
small pipe alone 3/4 1/40 30
both pipes together t
Now get the combined rate of both pipes together by adding their
rates:
. Fill that in:
number of
tanks or parts rate in
of tanks per time in
tanks filled minute minutes
small pipe in general 1 1/40 40
large pipe in general 1 1/25 25
small pipe alone 3/4 1/40 30
both pipes together 13/200 t
Fill in the part of a tank the two pipes together filled during
the t minutes when they were both open by multiplying the rate
times the time,
number of
tanks or parts rate in
of tanks per time in
tanks filled minute minutes
small pipe in general 1 1/40 40
large pipe in general 1 1/25 25
small pipe alone 3/4 1/40 30
both pipes together (13/200)t 13/200 t
Now the 3/4 of a tank which the small pipe filled during the 30
minutes PLUS the part of the tank which both pipes filled during
the t minutes must equal to 1 tank. So the equation is:
Can you solve that? If not post again asking how.
Answer: minutes or minutes.
Edwin