25 outlets working 6 hours a day, can empty a reservoir in 10 days. If only 15 outlets are operational and work for 4 hours a day, in how many days the reservoir can be emptied?

25 days

We can use the work formula for chain rule problems:

$\frac{M_1 \times D_1 \times H_1}{W_1} = \frac{M_2 \times D_2 \times H_2}{W_2}$

Where:

• $M$ = Number of outlets
• $D$ = Number of days
• $H$ = Hours worked per day
• $W$ = Total work (which is $1$ since it's the same reservoir in both cases)

Step 1: Plug in the given values

• Case 1: $M_1 = 25$, $H_1 = 6$, $D_1 = 10$
• Case 2: $M_2 = 15$, $H_2 = 4$, $D_2 = ?$

$25 \times 10 \times 6 = 15 \times D_2 \times 4$

Step 2: Simplify and solve for $D_2$

$1500 = 60 \times D_2$

$D_2 = \frac{1500}{60}$

$D_2 = 25 \text{ days}$