Who can solve it?

Fran94 , KS15 set up a proportion, and the answer is correct.

Maybe try it this way: to the standard Rate * Time = Work table, just add one more variable to the left hand side, thus

# of machines M * Rate * Time = Work

Manipulate the equation with four variables (MRT=W) the same way you would with three (RT=W).

Find each machine's individual rate. With the extra variable M, you simply manipulate

M * R * T = W

R = \(\frac{W}{(M * T)}\)

R = \(\frac{4}{(4 * 4)}\)

R = \(\frac{1}{4}\) = each machine's rate

Now use the rate to find the time for a different number of machines, and a different amount of work.

M * R * T = W

100 * \(\frac{1}{4}\) * T = 100

T = \(\frac{W}{(M * R)}\)

T = \(\frac{100}{\frac{100}{4}}\)

T = 100 * \(\frac{4}{100}\)

T = 4 minutes

(You could also notice that the LHS is 100/4 = 25, so RHS/LHS = 100/25 = 4 minutes)

Maybe try drawing the table (I do) with the extra variable, and doing the math. The proportional relationship should become clearer.

Does that help?

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