Nathaniel can weld a railing in 75 minutes. Brenda can weld a railing 25 minutes faster. If they work together, how many minutes does it take them to weld the railing?

Question

Avery Alexander · Accepted Answer

We will treat the times it takes them to weld the railing as rates and add them together.

All right, let's define the speeds first. Brenda can do one railing every 50 minutes (25 less than 75), while Nathaniel can do one every 75 minutes. Given that the two rates complement one another, we will add them. #(1" railing")/(75" minutes") +(1" railing")/(50" minutes")# We use the common denominator of #150 " minutes"#. #(1*color(green)2" railings")/(75*color(green)2" minutes") +(1*color(green)3" railings")/(50*color(green)3" minutes")# #(2" railings")/(150" minutes") +(3" railings")/(150" minutes")# #(5" railings")/(150" minutes")=(1" railing")/(30" minutes")# They weld the railing in #30" minutes"#.