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nina1390
15.04.2020 •
Mathematics
There is a reservoir with five channels bringing in water. If only the first channel is open, the reservoir can be filled in13 of a day. The second channel by itself will fill the reservoir in 1 day, the third channel in212 days, the fourth one in 3 days, and the fifth one in 5 days. If all the channels are open together, how long will it take to fill the reservoir?
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Ответ:
approximately 0.2 days
Step-by-step explanation:
Flow is defined as:
Q = V/t
where Q is flow, V is volume, and t is time
Let's call Vr to the volume of the reservoir, then for the first channel:
Q1 = Vr/t1
Replacing with t1 = 1/3 of day:
Q1 = Vr/(1/3) = 3*Vr
Similarly, or the other channels:
Q2 = Vr/1 = Vr
Q3 = Vr/(2 1/2) = 2/5*Vr
Q4 = Vr/3
Q5 = Vr/5
When all channels are open, the time needed to fill the reservoir is:
Vr = t*(Q1 + Q2 + Q3+ Q4 + Q5)
Replacing with the previous equivalences:
Vr = t*(3*Vr + Vr + 2/5*Vr+ Vr/3 + Vr/5)
Vr = t*4.93*Vr
1/4.93 = t
0.2 = t
Ответ: