Question

11. Two people are running around an oval track. They leave the starting point together. One completesthe track every 28 minutes. The second completes the track every 35 minutes. How long will it takefor them to both pass the starting point at the same time, if they both continue to run?

Answer 1

140 minutes

Step-by-step explanation

To find how long will it take for them to both pass the starting point at the same time, if one person completes the track in 28 minutes and the other completes it in 35 minutes, we have to find the lowest common multiple (LCM) of these two numbers.

To find the LCM, we can use the prime factorization method. First, write the prime factors of both numbers,

`\begin{gathered} 28:2*2*7 \\ 35:5*7 \end{gathered}`

Then, multiply all the prime factors as many times as they occur most often. If a factor occurs the same number of times in both numbers, then we only write it once. In this case,

`LCM=2*2*5*7=140`

Hence, it will take 140 minutes for both runners to pass the starting point at the same time.