On the ceiling of a cavern, a stalactite grows downward

.004

inches per year. Ten feet directly below on the cavern's floor, a stalagmite grows upward. 006

inches per year. How many years will it take them to meet?

The stalactites become 0.004 + 0.006 = 0.01 inches closer each year, and begin 10 feet apart, or 120 inches apart.

let y be the distance between them, and x be the number of years that go by:

y = - 0.01x + 120

We want to find where y = 0, where they meet:

0 = - 0.01x + 120 Add 0.01x to both sides

0.01x = 120 Multiply both sides by 100

x = 12,000

The stalagmite and stalactite will meet in 12,000 years