Answer:
It takes 8 minutes for each of them to have 28 liters
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Explanation:
- x = time that has elapsed (in minutes) since Jane started filling her jug
- y = amount of water in the jug (in liters)
x and y are nonnegative real numbers.
The equation for Jane is y = 3.5x since her faucet has a rate of 3.5 liters per min.
For example, if x = 2 minutes go by, then y = 3.5*x = 3.5*2 = 7 liters are filled up.
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We're told that after 1 minute Jane has started, Ariel has started to fill her jug. This must mean Ariel's time value is x-1. Whatever Jane's time value is, subtract off 1. This is because Jane has the 1 minute head start.
The equation for Ariel is y = 4(x-1) since her faucet has a rate of 4 liters per min.
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The system of equations to solve is
[tex]\begin{cases}y = 3.5x\\y = 4(x-1)\end{cases}[/tex]
Let's apply substitution to solve for x.
y = 3.5x
4(x-1) = 3.5x
4x-4 = 3.5x
4x-3.5x = 4
0.5x = 4
x = 4/0.5
x = 8
At the 8 minute mark (ie 8 minutes after Jane starts), is when the two jugs will have the same amount of water.
- Jane: y = 3.5x = 3.5*8 = 28
- Ariel: y = 4(x-1) = 4(8-1) = 4(7) = 28
Both of them have 28 liters each.
