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?

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.