A pool can hold 850 gallons, It now has 598 gallons of water and is being filled at the rate shown. How many more minutes, m , can water continue to flow into the pool before it overflows? Write and solve an inequality.

To find the time before the pool overflows, we start by determining how much more water the pool can hold. The pool can hold 850 gallons and currently has 598 gallons. Therefore, the remaining capacity is 850 - 598 = 252 gallons. Let’s denote the rate at which water is filling the pool as r gallons per minute. To express the number of minutes (m) before the pool overflows, we set up the inequality: \[ r \cdot m \leq 252 \] Now, solving for m gives us: \[ m \leq \frac{252}{r} \] This ensures that the total water after m minutes will not exceed 850 gallons. If you plug in the rate r, you can calculate the exact number of minutes left before your pool decides to take a little “bath” and overflow! Now, remember to keep that hose in check. If water fills too fast, you might end up with a backyard water feature you didn't plan for!