two cars moves around a circle of circumference 20m with speed of 5m/s and 15m/s, if the positions of these cars are observed every integer seconds, after how many seconds will the cars occupy the same position.
Plz maths work needed than
To find the time at which the two cars occupy the same position on the circle, we need to consider their relative speeds.
Let's assume that the car moving at 5 m/s starts at a reference point (position 0) on the circle. Since the circumference of the circle is 20 m, after 1 second, the car would have covered a distance of 5 m (5 m/s * 1 s). Therefore, after T seconds, the car moving at 5 m/s will be at position 5T on the circle.
Similarly, the car moving at 15 m/s will cover a distance of 15T on the circle after T seconds.
For the two cars to be at the same position, their distances traveled on the circle must be an integer multiple of the circumference (20 m). In other words, we need to find a positive integer T that satisfies the equation:
5T = 15T (mod 20)
To solve this equation, we can simplify it by dividing both sides by T:
5 = 15 (mod 20)
Now, we can solve for T by finding the least common multiple (LCM) of 5 and 15:
LCM(5, 15) = 15
Therefore, the two cars will occupy the same position on the circle after 15 seconds.
Note: If you're not familiar with modular arithmetic, the equation "5 = 15 (mod 20)" means that 5 and 15 have the same remainder when divided by 20.