In 1979, a river was 2727 feet below a bridge. By 1989 it was only 1818 feet below. Assuming the rate of rise is constant, write an expression for the distance from the bridge to the river. In what year will the river reach the height of the bridge?

1 Answer
Jan 18, 2018

The answer is 27-9/10t27910t and 20092009

Explanation:

We are starting, at t=0t=0 (1979), with the river at 27 feet below the bridge, so it makes sense that this is our starting point.

From there, we discover that the level changed by 27-18=92718=9 feet in the 1989-1979=1019891979=10 year period between 1979 and 1989.

That means that the rate of rise is 99 feet every 1010 years, so we can express that as 9/10t910t.

To find the year in which the river reaches the bridge, we know that the distance between them will be 00 at that time.

0=27-9/10t0=27910t

Solving this gives t=30t=30 years, which when added to the start year of 19791979 leads to 20092009.