There are two photocopy machines in a office. The first machine produces 5 copies in 8 seconds. The second produces 16 copies in 24 seconds. Are the two machines making copies at the same rate? Show your work and explain how you determined your answer.

No, a rate of 5 copies for every 8 seconds is not the same rate as the simplified rate of the second machine of 2 copies for every 3 seconds

Step-by-step explanation:

If they are producing at the same rate then for every second they should produce the same amount.

Let's test that.

WORK:

Machine 1 produces 5 copies in 8 seconds which is 5copies/8seconds or 5/8

Machine 2 produces 16 copies in 24 seconds which is 16 copies/24 seconds or 16/24 which simplifies to 2/3

Understanding the concept

If 5/8 were the same as 2/3, then 5/8 would be able to be reduced to 2/3, that's why we don't simplify fractions using decimals. 2/3 is 0.666666... and 5/8 is 0.625. Though irrelevant to solving it's useful to understand why it's always true that if the reduced fractions are different they never are the same.

Hope this helps,