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?
Answer & explanation
Correct answer: option 4
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 $D_2$
$1500 = 60 \times D_2$
$D_2 = \frac{1500}{60}$
$D_2 = 25 \text{ days}$