Explanation

To determine how many days a mechanic takes to assemble 64 machines, we can use the concept of rates. The rate of work is the number of machines assembled per unit of time.

In this case, the mechanic assembles 8 machines in 3 days, so the rate of work is 8 machines/3 days. To find out how many days he takes to assemble 64 machines, we can set up an equation using the rate of work:

64 machines / (8 machines/3 days) = x days

Solving for x we can get the number of days the mechanic takes to assemble 64 machines.

x = (64 machines) * (3 days) / 8 machines x = 24 days

So the mechanic takes 24 days to assemble 64 machines if he assembles 8 machines in 3 days.