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?

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