Question

At time t = 0, water begins to drip out of a pipe

nto an empty bucket. After 56 minutes, 8 inches
of water are in the bucket. What linear function
n the form y = mx + b represents the amount of
water in inches, w, in the bucket after t minutes?

Answer 1

Explanation:

w = t/7

at the beginning we 0 inches of water.

after 56 minutes we have 8 inches of water.

that is a ratio of 56 minutes / 8 inches = 7/1 = 1 / 1/7.

so, in 1 minute we get 1/7 inch of water.

in 2 minutes 2×1/7 = 2/7.

in 3 minutes 3×1/7 = 3/7.

...

hence the equation.

Answer 2

• y = t/7

Explanation:

Given

• Start time t = 0,
• Start level y = 0,
• Level of y = 8 in after t = 56 min

Solution

Find the value of m and b in the equation y = mx + b.

The value of b = 0, since there is no level in the bucket initially.

Find the value of m, the slope:

• 8 = 56m,
• m = 8/56
• m = 1/7

So the equation is:

• y = (1/7)t + 0

or

• y = t/7