Question

One spillway can empty the reservoir behind Beaver Creek Dam in 5 days and a second spillway can empty it in 7 days. How long will it take to empty the reservoir if both spillways are used at the same time? Must change the fractional day to hours.

Answer 1

Working together, both spillways can empty the reservoir in 70 hours. We find this by calculating the combined rate of the spillways and then finding its reciprocal to get the total time.

Step-by-step explanation:

The problem at hand involves calculating the time it would take to empty a reservoir using the combined flow rates of two spillways, a typical rate and time problem in mathematics. If one spillway can empty the reservoir in 5 days and the other in 7 days, they have rates of ⅖ and ⅗ respectively of the reservoir per day when working on their own. To find the combined rate, we add these two rates together:

⅖ + ⅗ = ⅞

Thus, the combined rate of both spillways is ⅞ of the reservoir per day. To find the total time, we take the reciprocal of the combined rate:

Time = ⅞-1 = 35/12 days

Therefore, if both spillways are used together, it will take them 35/12 days to empty the reservoir. Converting the fraction of a day to hours:

35/12 days * 24 hours/day = 70 hours

So, using both spillways at once will empty the reservoir in 70 hours. Remember to always consider the individual flow rates of each component and their cumulative effect when they are used in tandem.