Answer: Ken will run 3 laps and Hamid will run 4 laps till they next meet at the start line.
Explanation:
Given: It t takes Ken 80 seconds to complete a lap and Hamid 60 seconds to complete a lap .
To find when they, meet we need to find the least common multiple of 80 and 60.
Since
![80=4*20\\60=3*20](https://img.qammunity.org/2020/formulas/mathematics/middle-school/2zjevb699fw6vllxuvs3ee6bvg05j4quan.png)
Therefore, LCM(60,80)=
![4*3*20=240](https://img.qammunity.org/2020/formulas/mathematics/middle-school/xu2wqd1sb18dyd8y3qfpzhuiq4vfuwq2xh.png)
Thus they will meet after 240 seconds.
So the number of laps completed by Ken=
![(240)/(80)=3](https://img.qammunity.org/2020/formulas/mathematics/middle-school/mzyzi7mg28erhlt1eags7vimzemlsp2rdi.png)
The number of laps completed by Hamid=
![(240)/(60)=4](https://img.qammunity.org/2020/formulas/mathematics/middle-school/puczrvygdttxt66pznybinbju2uzr5n3fk.png)