A small pool is being drained. There are 1,320 gallons of water remaining in the pool after 2 minutes and 1,040 gallons after 9 minutes. How long would it take for the pool to be completely drained?(1 point) minutes
We can set up a linear equation to represent the relationship between the time and the remaining gallons of water in the pool.
Let x be the number of minutes it would take for the pool to be completely drained.
Using the given information, we can form two equations:
The equation for 2 minutes: y = mx + b
1320 = 2m + b
The equation for 9 minutes: y = mx + b
1040 = 9m + b
We can subtract the two equations to eliminate b
1320 - 1040 = (2m + b) - (9m + b)
280 = 9m - 2m
280 = 7m
Dividing both sides by 7 gives m = 280/7 = 40
Using the value of m in either of the equations, we can find b.
1320 = 2m + b
1320 = 2(40) + b
1320 = 80 + b
Subtracting 80 from both sides gives 1240 = b
Therefore, the equation for the remaining gallons of water y in terms of the time x is:
y = 40x + 1240
To find when the pool would be completely drained (when y = 0), we can substitute y = 0 into the equation and solve for x:
0 = 40x + 1240
Rearranging the equation gives 40x = -1240
Dividing both sides by 40 gives x = -31
Since time cannot be negative, the pool would be completely drained after 31 minutes. Answer: \boxed{31}.