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)
A and B have to travel from place P to place Q following the same route in their respective cars. A drives at $60$ kmph while B drives at $80$ kmph. Find the time taken by B to reach place Q if A takes $12$ hrs.
On a straight road, a bus is $60$ km ahead of a car running in the same direction. After $3$ hours, the car is $90$ km ahead of the bus. If the speed of the bus is $45$ km/h, then what is the speed of the car (in km/h)?
A train running at the speed of $90$ kmph crosses a $250$ m long platform in $26$ seconds. What is the length of the train (in m)?
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 car travels a total distance L. It travels half the distance with speed $v_1$ and the other half with speed $v_2$. The average speed of the car is :
