Answer:
45 minutes
Step-by-step explanation:
Let, after time
minutes, they meet again at the same point.
In time
minutes, let Sony completes x lap while Iogan completes y laps. Note that x and y must be the counting numbers.
As Sonny took 15 minutes to drive 1 lap, so,
![t=15x\cdots(i)](https://tex.z-dn.net/?f=t%3D15x%5Ccdots%28i%29)
While Iogan Sonny took 9 minutes to drive 1 lap, so,
![t=9y](https://tex.z-dn.net/?f=t%3D9y)
[from equation (i)]
![\Rightarrow \frac {x}{y}=\frac{9}{15}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%20%7Bx%7D%7By%7D%3D%5Cfrac%7B9%7D%7B15%7D)
![\Rightarrow \frac {x}{y}=\frac{3}{5}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%20%7Bx%7D%7By%7D%3D%5Cfrac%7B3%7D%7B5%7D)
As x,y must be counting number, so
(x,y)=(3,5),(6,10),...,(3n,5n) where n is a positive integer.
So, the minimum number of laps required are
x=3 and y=5 (when they meet for the first time)
Now, from equation (i),
The time required to meet them for the first time, t=15x3=45 minutes.