Two brothers are digging a drainage ditch for a french drain around their home. The ditch is to be 2 feet deep, 1 foot wide, and 40 feet long. The older brother can dig the ditch in 14 hours. The younger brother can dig the ditch in 17 hours. How long will the two brothers working together take to dig the ditch? (Round your answer to the nearest tenth.)

The two brothers working together will take 7.7 hours to dig the entire ditch.

Explanation:

Assuming T to be the total amount of time taken by both brothers working together, we can say

1/T ditch/hour to be the rate at which both brothers dig the ditch together 1/14 ditch/hour to be the rate at which the older brother digs the ditch 1/17 ditch/hour to be the rate at which the younger brother digs the ditch

So the rate at which both brothers dig the ditch can be calculated by the equation,

1/T = 1/14 + 1/17

T = 238/31 = 7.7 (rounded off to the nearest tenth)