Question

Manicurist #1 is filing nails at the rate of 1

every 20 seconds. Manicurist #2, on the other
hand (no pun intended), is only filing nails at the
rate of 1 every 30 seconds. If they work
together, how many seconds will it take them to
file 40 nails?

Answer 1

480 Seconds

Explanation:

To find how long it would take, with them filing at the same time we just have to combine their speed into one equation. Here is how I looked at it.

Let's try to make this into an algebraic equation, 1 nail every 20 seconds can be represented as 1/20x, or 0.05x

1 nail every 30 seconds would be 1/30x, or 0.03333x

We combine these and we get 1/12x or 0.08333x

Now, we just set up the equation. x(1/12) = 40

x/12 = 40

x*12 = 40*12

x = 480