Question

1. mike and ted are having a push - up competition during basketball practice. mike does 15 push - ups in the time it takes ted to complete 10. when ted has finished 40 push - ups, how many has mike done?

Explanation:

Step1: Determine the ratio of Mike's push - ups to Ted's push - ups

The ratio of Mike's push - ups to Ted's push - ups in the same time is $\frac{15}{10}=\frac{3}{2}$. This means that for every 2 push - ups Ted does, Mike does 3.

Step2: Find out how many sets of 10 push - ups Ted has done when he does 40 push - ups

To find the number of sets, we divide the total number of push - ups Ted has done (40) by the number of push - ups in each set (10). So, $40\div10 = 4$ sets.

Step3: Calculate the number of push - ups Mike has done

Since in each set (where Ted does 10 push - ups) Mike does 15 push - ups, and there are 4 sets, we multiply the number of push - ups Mike does per set (15) by the number of sets (4). So, $15\times4=60$. We can also use the ratio. Let $x$ be the number of push - ups Mike does when Ted does 40. Using the proportion $\frac{15}{10}=\frac{x}{40}$, we cross - multiply: $10x = 15\times40$, then $x=\frac{15\times40}{10}=60$.

Answer:

60