Math Is Fun Forum

Bob bundy - thankyouthankyouthankyou!

I've been banging my head into the wall for far too many times the last couple of days, trying to figure out the solution, but after reading (and re-reading) your post several times it finally dawned on me. It felt like something just *clicked* in place and I "leveled up". Gotta love math!

For posterity's sake I'll post the solutions:

Like bob bundy wrote, the trick is to use the derived formula and set the descending rate to -4 (since the height h will be decreasing), and then solve for x. We have:

The solution is to realize that when the top and bottom are moving at the same rate, then dh/dt will be equal to dx/dt. From previously, we have the formula:

If we solve for x, dx/dt goes to the other side as the reciprocal:

Then substituting h:

Once again, thanks for the help!