Machine A, working alone at its constant rate, produces x pounds of peanut butter in 1 minutes. Machine B, working alone at its constant rate, produces x pounds of peanut butter i 18 minutes. How many minutes will it take machines A and B, working simultaneously at their respective constant rates, to produce x pounds of peanut butter? (Work & Time)

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

A can produce in 12 minutes x pound of peanut butter
A can produce in 1 minute $\frac{x}{12}$ pound of peanut butter
Again, B can produce in 18 minutes x pound of peanut butter

B can produce in 1 minute $\frac{x}{18}$ pound of peanut butter

So, in 1 minute (A + B) can produce = $(\frac{x}{12} + \frac{x}{18}) = (\frac{3 x + 2 x}{36}) = \frac{5 x}{36}$ pounds.

Now, $\frac{5 x}{36}$ pounds can be produced by (A + B) in = 1 minute
x pounds can be produced by (A + B) in = $\frac{36 \times x}{5 x} = 7.2$ minutes = 7 minutes 12 seconds. (ans.)