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Question 99921: You are running water into a laundry sink to get a mixture that is one-half hot water and one-half cold water. The hot water flows more slowly, at a rate of 7.8 liters per minute, so you turn it on first. Two minutes later, you also turn on the cold water which flows at a rate of 12.3 liters per minute. You want to know how long to wait before turning the two faucets off.
a. Let t represent the number of minutes the hot water is on. Write a variable expression for the amount of time the cold water is on.
b. Write an equation that models the situation. Then solve the equation.
c. Interpret your solution. If the solution is a decimal, decide what form of the number is most appropriate. Explain your choice
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! You are running water into a laundry sink to get a mixture that is one-half hot water and one-half cold water. The hot water flows more slowly, at a rate of 7.8 liters per minute, so you turn it on first. Two minutes later, you also turn on the cold water which flows at a rate of 12.3 liters per minute. You want to know how long to wait before turning the two faucets off.
:
a. Let t represent the number of minutes the hot water is on. Write a variable expression for the amount of time the cold water is on.
:
Cold water time = (t - 2)
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b. Write an equation that models the situation. Then solve the equation.
:
cold water amt = hot water amt
12.3(t-2) = 7.8t
12.3t - 24.6 = 7.8t
12.3t - 7.8t = + 24.6
4.5t = 24.6
t = 24.6/4.5
t = 5.467 min turn off both faucets
:
Check:
Cold water is on for 5.467 - 2 = 3.467
Check for equal amts
5.467 * 7.8 = 42.6 liters
3.467 * 12.3 = 42.6 liters also confirms our solution
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c. Interpret your solution. If the solution is a decimal, decide what form of the number is most appropriate. Explain your choice
Since the flow rate is given in decimals, use decimals.
I'll let you interpret the solution.
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