a very hard problem (at least for me)

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Hi. I need a lot of help on this question. I've been trying to figure out how to solve this problem for days and still havent found the answer. :(

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. :D
 
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.
Click to expand...

Waht have you done so far? Please show us.

This problem is similar to a distance problem: If one person starts walking at a certain speed, and then 2 mins later another person starts jogging after them, when will the jogger catch the walker?

The distance problem would use d = rt. Each person has a different r (rate of speed). If the first person started walking at time t = 0, then the second person started jogging at time t = 2.

The tub of water problem is just the same, only the r is for rate of flow (volume per unit time). Therefore use V = rt. Write the eqn for each faucet (hot and cold). One-half hot and one-half cold means the volumes must be the same (like the jogger catching the walker, the distances are the same.)

Hope this helps.
 
so would it be rt = rt? or no? and then the time for the hot water would be 0? but if it would be 0 then when you multiply..the answer would be 0 :? whats eqn? equation?

I tried to do a proportion but i dont think that it helps any:

2 t 12.3t = 7.8 (2)
----- = ----- 12.3t = 15.6
12.3 7.8 t = 1.27
 
2 -- t
-- = --
12.3 -- 7.8


12.3t = 7.8 (2)
12.3t = 15.6
t = 1.27

is that a little better? its kinda still messed up but...
 
Good, you’re getting closer. Hot water volume as a function of time is this:

Vh = 7.8*t

Cold water volume is this:

Vc = 12.3*(t – 2)

Why do we use the term (t-2)? Because at time t = 2, we’re just turning on the cold water, and the amount of cold water in the tub at that moment is still zero. So at time t = 10, for example, Vh = 78 liters, and Vc = 12.3*(10-8) = 98.4 l. To solve for equal volumes of hot and cold, set Vh = Vc, and we get:

7.8*t = 12.3*(t-2)
 
Hello, BurnedAngel171

You are running water into a sink to get a mixture that is half hot water and half cold water.
The hot water flows more slowly, at a rate of 7.8 liters/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/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.
(a) Write a variable expression for the amount of time the cold water is on.
(b) Write an equation that models the situation.
(c) Then solve the equation.
(d) Interpret your solution.
(e) If the solution is a decimal, decide to which place you would round the numbers.
(f) Explain your choice. . . . Is that all they want?
Click to expand...
They said: let t = number of minutes the hot water is on.

Since the cold water was turned two minutes later,
. . (a) . t - 2 = number of minutes the cold water is on.


Hot water runs at 7.8 L/m for t minutes.
. . There will be 7.8t liters of hot water.

Cold water runs at 12.3 L/m for t-2 minutes.
. . There will be 12.3(t-2) liters of cold water.

These two amounts are to be equal: . (b) . 12.3(t - 2) .= .7.8t


We have: . 12.3t - 24.6 .= .7.8t
. . . . . . . . . .12.3t - 7.8t .= .24.6
. . . . . . . . . . . . . . . 4.5t .= .24.6
. . . . . . . . . . . . . . (c) . t .= .24.6/4.5 .= .5.46666....

(d) .The hot water is turned on.
. . . Two minutes later, the cold water is turned on.
. . . 3 and 7/15 minutes later, both faucets are turned off simultanrously.
. . . There will be equal amounts of hot and cold water . . . exactly 42.64 liters of each.

(e) .The answer is a decimal, but I would not round it off.

(f) . 5 and 7/15 minutes is <u>exactly</u> 5 minutes and 28 seconds.
 
ok...im confused with d) how do you get 3 and 7/15 minutes and 42.64 liters?

i checked out 12.3 (t-2) = 7.8t but it doesnt check out completely...should i use 5.46 or 5.47?

where does the 3 and 7/15 come from?? im totally stumped there
 
where does the 3 and 7/15 come from?? im totally stumped there
Click to expand...

It's just the amount of time the cold water is on. The t we are solving for is the time the hot water is on, 5 7/15 minutes.
 
but when i try to do it..the answer doesnt come out to be 3 and 7/15 or 5 and 7/15...and it doesnt come out to be exactly 42.64
 
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