Question

Working at their respective constant rates, machine a makes 100 copies in 12 minutes and machine b makes 150 copies in 10 minutes. if these machines work simultaneously at their respective rates for 30 minutes, what is the total number of copies that they will produce? (a) 250 (b) 425 (c) 675 (d) 700 (e) 750

Answer 1

Rate at which machine a makes copies = 100/12 = 8 1/3 copies / minute

For machine b this rate is 150/10 = 15 copies/minute

So in 30 minutes they both make 30 * 15 + 30 * 8 1/3

= 700 answer

Answer 2

Since both machines maintain their rate, the number of copies made and the elapsed time are proportional. This means that we can write a proportion like

$\text{time}_1 : \text{copies in time}_1 = \text{time}_2 : \text{copies in time}_2$

We know the performance of machine a for 12 minutes, and we want those for 30 minutes: the proportion becomes

$12 : 100 = 30 : x \iff x = \dfrac{100\cdot 30}{12} = \dfrac{3000}{12} = 250$

Similarly, we have for machine b

$10 : 150 = 30 : x \iff x = \dfrac{150\cdot 30}{10} = \dfrac{4500}{10} = 450$

So, together, the two machines make

$250+450 = 700$

copies.