stupid laundry

Ive been struggling with this problem for quite sometime now :shock: ..... any help is greatly appreciated.


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. 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. Write an equation that models the situation. Then solve the equation. Interpret you solution. If the solution is a decimal, decide to which place you would round the numbers. Explain your choice.

I would greatly appreciate anyones help on this.

If the hot is on t minutes the cold is on t-2 minutes.
The amount of hot water is 7.8t
The amount of cold water is 12.3(t-2)
You want equal amounts so
7.8t=12.3(t-2)
Solve for t

If the hot water has been on for 3 minutes, how long has the cold water been on?

If the hot water has been on for 5 minutes, how long has the cold water been on?

If the hot water has been on for 10 minutes, how long has the cold water been on?

If the hot water has been on for t minutes, how long has the cold water been on?

At 7.8 L/min, if the hot water has been on for 2 minutes, how many liters of hot water have been poured into the sink?

At 7.8 L/min, if the hot water has been on for 4 minutes, how many liters of hot water have been poured into the sink?

At 7.8 L/min, if the hot water has been on for 10 minutes, how many liters of hot water have been poured into the sink?

At 7.8 L/min, if the hot water has been on for t minutes, how many liters of hot water have been poured into the sink?

Following the same reasoning, how many liters of cold water have been poured into the sink?

Set the two expressions equal, and solve for the time t.

Eliz.

thanks very much helped a ton