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

Answer:

45 minutes

Step-by-step 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)]

$\Rightarrow \frac {x}{y}=\frac{9}{15}$

$\Rightarrow \frac {x}{y}=\frac{3}{5}$

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.