Every few minutes, Cindy measures the height of water, in inches, in a bucket while it is being filled at a constant rate. She makes a graph of her results. Two points on her graph are (5,6) and (8,9).
Meanwhile, Ben is draining another bucket of water at a constant rate, measuring the height of the water, in inches, every few minutes. Two points on the graph of his results are (0,5) and (6,3).
After how many minutes, x, will the height of the water in inches, y, be the same in both buckets?
The height of water in Cindy's bucket and the height of water in Ben's bucket will both be inches at minutes.
The answer is 4 inches in 3 min
urtdu
(5,6), (8,9). m = (9-6)/(8-5) = 1, Y = mx + b = 6, 1*5 + b = 6, b = 1, Y = x + 1.
(0,5), (6,3). m = (3-5)/(6-0) = -1/3, Y = mx + b = 5, (-1/3)0 + b = 5, b = 5, Y = (-1/3)x + 5.
x + 1 = (-1/3)x + 5,
x+1 = -x/3 + 5, x + x/3 = 4,
Multiply both sides by 3:
3x + x = 12, X = 3 Min.