sYstems
Solving a value mixture problem using a system of linear...
Michael
The Foster family and the Young family each used their sprinklers last summer. The water output rate for the Foster family's sprinkler was $15 \mathrm{~L}$ per hour. The water output rate for the Young family's sprinkler was $35 \mathrm{~L}$ per hour. The families used their sprinklers for a combined total of 40 hours, resulting in a total water output of 900 L. How long was each sprinkler used?
Foster family's sprinkler: Ø1 hours
Young family's sprinkler: $\square$ hours
?
Español
Answer
Final Answer: The Foster family's sprinkler was used for \(\boxed{25}\) hours and the Young family's sprinkler was used for \(\boxed{15}\) hours.
Step 1 ：Translate the problem into a system of linear equations. Let's denote the time the Foster family's sprinkler was used as x and the time the Young family's sprinkler was used as y. Then we have two equations: \(x + y = 40\) (total time) and \(15x + 35y = 900\) (total water output).
Step 2 ：Solve the system of equations to find the values of x and y. The solution is \(x = 25\), \(y = 15\).
Step 3 ：Final Answer: The Foster family's sprinkler was used for \(\boxed{25}\) hours and the Young family's sprinkler was used for \(\boxed{15}\) hours.
