Question: User: Question 6:
Two sump pumps working at the same rate drain a flooded basement in 69 hours. How long does it take 3 pumps working at the same rate to drain the basement?
Question 7:
A solution contains 1/4 ounce acid and 8 1/2 ounces of water. For the same
strength solution, how much acid should be mixed with 12 3/4 ounces of water?
Question 8:
A piece of lumber 2.8 meters long weighs 24.5 kilograms. A piece 0.8 meter long
is cut from the 2.8-meter length. Determine the weight of the 0.8-meter piece.
Question 9:
The volume of gas decreases as pressure increases. When pressure is 45.0 units,
the volume is 9.0 units. Find the proportionality constant for this situation.
1. **State the problem:** Two sump pumps working together drain a basement in $69$ hours. We want to find how long $3$ pumps working at the same rate take to drain it.
2. **Formula and concept:** The work rate of pumps adds up. If $2$ pumps take $69$ hours, their combined rate is $\frac{1}{69}$ of the job per hour.
3. **Calculate rate per pump:** Rate per pump $= \frac{1}{69} \div 2 = \frac{1}{2 \times 69} = \frac{1}{138}$ jobs per hour.
4. **Calculate rate for 3 pumps:** Rate for $3$ pumps $= 3 \times \frac{1}{138} = \frac{3}{138} = \frac{1}{46}$ jobs per hour.
5. **Find time for 3 pumps:** Time $= \frac{1}{\text{rate}} = \frac{1}{\frac{1}{46}} = 46$ hours.
**Final answer:** It takes $3$ pumps $46$ hours to drain the basement.