Math

Question Two families used sprinklers last summer. Miller family used it for 15 hours, Simmons family for 20 hours. Total water output was 1000 L1000 \mathrm{~L}. If the sum of their rates was 60 L60 \mathrm{~L} per hour, what were the individual water output rates? Let M=M = Miller's rate (L/h)(L / h) and S=S = Simmons' rate (L/h)(L / h).

Studdy Solution

STEP 1

Assumptions1. The Miller family's sprinkler was used for15 hours. . The Simmons family's sprinkler was used for20 hours.
3. The combined total output of water was1000 L.
4. The sum of the two rates was60 L/h.
5. M represents the water output for the Miller family's sprinkler in L/h.
6. represents the water output for the Simmons family's sprinkler in L/h.

STEP 2

We can form two equations based on the given information. The first equation is based on the total output of water, and the second equation is based on the sum of the two rates.
The first equation can be formed as followsM×15+×20=1000M \times15 + \times20 =1000This equation represents the total output of water from the two sprinklers.

STEP 3

The second equation can be formed as followsM+=60M + =60This equation represents the sum of the two rates.

STEP 4

So, the system of equations that models this scenario is\begin{align*} M \times15 + \times20 &=1000 \\ M + &=60\end{align*}

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