# Math Help - leaky bucket , work

1. ## leaky bucket , work

A leaky bucket weights 7 lb and a rope of neglible weight are used to draw water from a well that is 306 ft deep. The bucket is filled with 47 lb of water and is pulled up at a rate of 3 ft/sec, but water leaks out of the bucket at a rate of 0.5 lb/sec. Find the word done in pulling the bucket to the top of the well (in ft-lb)

Have a random point y, time to get to y is y/3 sec. Amt of water lost is .5y/3 lb. Total weight of water and bucket is 54. so total weight lost is 54-.5y/3

I set up the integral from 0 to 306 of the above expression and I'm getting the wrong answer.

What am I missing?

2. Originally Posted by sheridan

I set up the integral from 0 to 306 of the above expression and I'm getting the wrong answer.

What am I missing?

Here is the problem. The bucket is empty 94 seconds(@ 282ft) after you start

$\int_{0}^{282}\left( -\frac{1}{6}x+54\right)dx+\int_{282}^{306}7dx
$

Good luck.