Runners Meeting at Start Line Problem
The problem asks for the time when two runners, who complete laps in 6 minutes and 8 minutes respectively, will meet again at the starting point. This occurs when the elapsed time is a multiple of both individual lap times.
Calculating Meeting Time
To find the first time they meet again at the start line, we need to find the Least Common Multiple (LCM) of their lap times, which are 6 minutes and 8 minutes.
Step 1: Find the prime factorization of each lap time.
- $6 = 2 \times 3$
- $8 = 2 \times 2 \times 2 = 2^3$
Step 2: Calculate the LCM by taking the highest power of each prime factor present in either factorization.
- The prime factors are 2 and 3.
- The highest power of 2 is $2^3$.
- The highest power of 3 is $3^1$.
- LCM$(6, 8) = 2^3 \times 3^1 = 8 \times 3 = 24$.
Therefore, the runners will meet again at the start line for the first time after 24 minutes.
Important Questions from Speed Time & Distance (Notes)
- Ajay walks at a speed of 4 km/hr. He doubles his speed after reaching exactly half way. He walks for 12 hours in all. What is the total distance travelled by him ?
With a certain set of diameters, a tractor's front wheels make 2 revolutions (revs) for every 1 revolution of the rear wheels. The effect of changing wheel diameter(s) is shown in the following plot.
In this context, which of the following statements is CORRECT?- A train travels from Karnal to Kurukshetra at a speed of $90$ km/hr and returns at a speed of $92$ km/hr. If it takes $182$ hours for total travel, then find the distance between Karnal to Kurukshetra. (In Km)
A car covers 4 successive stretches of 3 km each at speed of 10 kmph, 20 kmph, 30 kmph and 60 kmph respectively. The average speed of the car for the entire journey is:
- A cyclist travels at 18 km/hr for 2.5 hours. What distance does he cover?
