Answer:
The smaller tap took 4 hours and 52 minutes, and the larger tap took 4 hours and 44 minutes.
Step-by-step explanation:
Let x represent the time that the smaller tap took to fill the tank.
Let y represent the time that the larger tap took to fill the tank.
Find two equations in the problem.
(I use asterisks for multiplication and slashes for division)
x + y = (9*60)+36 (1)
y = x - 8 (2)
Solve by the method of substitution.
sub y = x - 8 into equation 1.
x + y = (9*60)+36
x + (x - 8) = 540 + 36
x + x - 8 = 576
2x - 8 = 576
2x - 8 + 8 = 576 + 8
2x = 584
Divide both sides by 2 to isolate x.
x = 292 minutes
We will convert into hours at the end.
sub x = 292 into equation 1.
x + y = 576 <------I solved the right side to make it easier to work with
292 + y = 576
292 - 292 + y = 576 - 292
y = 284
Convert into hours.
x = 292 / 60
60 goes into 292 four times - calculate the remainder to find the number of minutes.
292-240=52
x = 4 hours 52 minutes
y = 284/60
60 goes into 284 four times- calculate the remainder to find the number of minutes.
284-240=44
y = 4 hours 44 minutes
Therefore, the larger tap took 4 hours and 44 minutes to fill the tank, and the smaller tap took 4 hours and 52 minutes.