Show an equation and a solution for the problem. It takes John 20 hours to paint a building. It takes Sam 15 hours to paint the same building. How long will it take for them to paint the building if they work together, with Sam starting one hour later than John? Round to the nearest tenth.

Question

anonymous · Answer

John does 1/20 of the job in 1 hour, while Sam does 1/15 of the job in one hour.
We are looking for x = the time they work together.
However, John began 1 hour before Sam, which means he was working now for (x+1) hours.
Since (rate per hour)(time in hours) = work done
then,
(time of Sam)(rate of Sam) + (time of John)(rate of John) = 1, since they are working on one whole job.

therefore:
(x)(1/15)+(x+1)(1/20)=1
where x = time in hours.
Just solve for the unknown and you are good to go. :)