# Math Help - [SOLVED] Work

1. ## [SOLVED] Work

A bucket is being lifted to 20 ft in the air and starts with off 16lbs of water and is leaking at a constant rate. It finishes draining just as it reaches the top. How much work was spent lifting the water alone? (find the proportion of water left at elevation x ft)

the answer is 160 lbs ft but I got 3200
3200/4= 160 but I don't see how that would fit from the given information

2. Originally Posted by TAG16
A bucket is being lifted to 20 ft in the air and starts with off 16lbs of water and is leaking at a constant rate. It finishes draining just as it reaches the top. How much work was spent lifting the water alone? (find the proportion of water left at elevation x ft)

the answer is 160 lbs ft but I got 3200
3200/4= 160 but I don't see how that would fit from the given information
weight of water is changing at the rate of $-\frac{16}{20} = -\frac{4}{5}$ lbs/ft

$F = 16 - \frac{4}{5}h
$

$W = \int_0^{20} 16 - \frac{4}{5}h \, dh$

$W = \left[16h - \frac{2h^2}{5}\right]_0^{20}$

$W = 16(20) - \frac{2(20^2)}{5} = 320 - 160 = 160$ ft-lbs