Question

Sonny and logan where driving go carts around the track. Sony took 15 minutes to drive 1 lap, it took logan 9 minutes to drive around 1 lap. If two of then start at the same time and went there same speeds, after how many minutes would the 2 of them meet at the same point?

Answer 1

45 minutes

Explanation:

Let, after time
`t` minutes, they meet again at the same point.

In time
`t` 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)`

While Iogan Sonny took 9 minutes to drive 1 lap, so,

`t=9y`

`\Rightarrow 15x=9y` [from equation (i)]

`\Rightarrow \frac {x}{y}=(9)/(15)`

`\Rightarrow \frac {x}{y}=(3)/(5)`

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.