It takes Noah 3 hours to paint one side of a fence. It takes Gilberto 5 hours. How long would it take them if they worked together?

Question

It takes Noah 3 hours to paint one side of a fence.  It takes Gilberto 5 hours. How long  would it take them if they worked together?

Nathan Axel · Accepted Answer

I tried this but check it.

Let us say that the rates at which each one paints the surface (of area #1# for example) are: #1/3# and #1/5# to paint the same surface so together they will need a time #t#: #1/3t+1/5t=1# rearranging: #5t+3t=15# #8t=15# #t=15/8=1.875# less than 2 hours.

Jace Anderson · Answer

undefined To determine how long it would take Noah and Gilberto to paint the fence together, we can use the concept of work rates. Noah takes 3 hours to paint one side of the fence, so his work rate is 1/3 of the fence per hour. Gilberto takes 5 hours, so his work rate is 1/5 of the fence per hour.

To find their combined work rate, we add their individual work rates: 1/3 + 1/5 = 8/15.

Therefore, working together, Noah and Gilberto can paint 8/15 of the fence per hour.

To find the time it would take them to complete the entire fence, we can divide the total work (1) by their combined work rate (8/15):

1 / (8/15) = 15/8 = 1.875 hours.

So, it would take Noah and Gilberto approximately 1.875 hours, or 1 hour and 52.5 minutes, to paint the fence together.