Math Problem?

Question

There is a reservoir with five channels bringing in water. If only the first channel is open, the reservoir can be filled in 1/3 of a day. The second channel by itself will fill the reservoir in 1 day, the third in 2 and a half days, the fourth in 3 days and the fifth in 5 days. If all the channels are open together, how long will it take to fill the reservoir?

Answer 1

So this is hte equation you set up:
1/8+1/24+1/60+1/72+1/120=1/n ( teh denominators are the hrs. it take to fill them up)FInd a common denominator. In This case it is 360n. Multiply that to each side of the equation( what you get is the denominators canceling out).
And you get:
45n+15n+6n+5n+3n=360
74n=360 (divide by 74)
/74 /74
n=4.86 hrs.

Answer 2

Let us think a little about the flow.

So the total flow is:
Qt = Q1 + Q2 + Q3 + Q4 + Q5

Q is the ratio of the amount of liquid per time unit.
Say, 3 gallons per second, 7 liters per minute, etc.

Q = [ Vf - Vo ] / [ Tf - To ]
If we call Vf - Vo = V and Tf - To = T
V --> Delta Volume
T --> Delta Time

Q = V / T

Therefore,
Q1 = V1 / T1
Q2 = V2 / T2
Q3 = V3 / T3
Q4 = V4 / T4
Q5 = V5 / T5
Qt = Vt / Tt

But guess what? The reservoir is only one, so there is only one volume, one reservoir. It means that:
V1 = V2 = V3 = V4 = V5 = Vt

If we consider that the total flow is the sum of all the flows
of each channel, then we have:

Qt = Q1 + Q2 + Q3 + Q4 + Q5
Vt/Tt = V1/T1 + V2/T2 + V3/T3 + V4/T4 + V5/T5
Vt/Tt = Vt * [ 1/T1 + 1/T2 + 1/T3 + 1/T4 + 1/T5 ]
If we multiply this equation times 1/Vt
thence we have,

1/Tt = 1/T1 + 1/T2 + 1/T3 + 1/T4 + 1/T5

so theoretically,
Tt = 1 / { 1/T1 + 1/T2 + 1/T3 + 1/T4 + 1/T5 }

Now we go down to the values [in days]:
T1 = 1/3 day
T2 = 1 day
T3 = 2 1/2 days = 2.5 days = 5/2 days
T4 = 3 days
T5 = 5 days

So Tt is:
Tt = 1 / [ 3 + 1 + 2/5 + 1/3 + 1/5 ]
= 1 / [ ( 45 + 15 + 6 + 5 + 3 ) / 15 ]
= 1 / [ 74 / 15 ]
= 15 / 74 day
= 20.27027027% of a day

= 4 hrs 51 min 53.5135 seconds

Therefore the reservoir will take about 5 hrs to be filled in.

Answer 3

5/ 1/3= 4in a half.

Answer 4

you cant answer it unless you know the amount of water in the reservoir