Answer:
30 minutes
Step-by-step explanation:
Nathaniel can weld 1 rail in 75 minutes, so he welds 1R = 75 min, and Brenda can weld 1 rail in 50 minutes (25 minutes faster than Nathaniel), so she welds
1R = 50 min
We want to see how many minutes it takes them both, so we need to solve both problems for the minute unit
Nathaniel: (1/75)R = 1 min (he can do one seventy-fifth of a rail per minute)
Brenda: (1/50)R = 1 min (she can do one fiftieth of a rail per minute)
notice, the equation is 1/(minutes it takes them), and we want to see how long it takes both of them, so we get the equation:
1/75 + 1/50 = 1/x
Simplify the left side with common denominator of 57(50) = 3750
We get
125/3750 = 1/x
We can cross multiply to get rid of the fractions...
125x = 3750
Divide both sides by 125 to solve for x...
x = 30, so it would take them 30 minutes to weld a rail if they work together.
