Answer:
Below.
Step-by-step explanation:
Working together the rate is 80 + 120 = 200 gallons per minute.
(a) Time to fill tank = 6000 / 200 = 30 minutes.
(b) Let length of time the small pipe was used be x minutes , the the large pipe was used for is 60-x minutes.
Volume delivered by small pipe = y gallons, and by large pipe = 6000-y gallons.
Rate for small pipe = 80 = y/x.
Rate for large pipe = 120 = (6000-y) / 60-x.
y/x = 80
(6000-y) / 60-x = 120
From first equation y = 80x so:
6000 - 80 x = 7200 - 120x
40x = 1200
x = 30
So time for small pipe = 30 and time for large on = 30 minutes also.
C. In a similar way to part B:
y/x = 120
(6000-y) / 34 - x = 200
(6000-120x) / 34 - x = 200
6000 - 120x = 6800 - 200x
80x = 800 so the large pipe on its own took 10 minutes and the small pipe was used for 34 - 10 = 24 minutes.
