To find the distance the faster motorcyclist travels to overtake the slower one, we need to determine their speeds and the time it takes to close the gap.
Step 1: Calculate the Faster Motorcyclist's Speed
The speeds are in the ratio $5:3$. The slower motorcyclist's speed ($S_{slow}$) is 12 km/h. Let the faster motorcyclist's speed be $S_{fast}$.
We set up the proportion:
$ \frac{S_{fast}}{S_{slow}} = \frac{5}{3} $Substitute the known speed:
$ \frac{S_{fast}}{12 \text{ km/h}} = \frac{5}{3} $Solve for $S_{fast}$:
$ S_{fast} = \frac{5}{3} \times 12 \text{ km/h} $ $ S_{fast} = 5 \times 4 \text{ km/h} $ $ S_{fast} = 20 \text{ km/h} $The faster motorcyclist travels at 20 km/h.
Step 2: Calculate the Time to Overtake
The slower motorcyclist has a 24 km head start. The faster motorcyclist needs to close this distance.
The relative speed at which the faster motorcyclist catches up is the difference between their speeds:
$ S_{relative} = S_{fast} - S_{slow} $ $ S_{relative} = 20 \text{ km/h} - 12 \text{ km/h} $ $ S_{relative} = 8 \text{ km/h} $The time required to cover the 24 km gap is calculated using:
$ \text{Time} = \frac{\text{Distance Gap}}{S_{relative}} $ $ \text{Time} = \frac{24 \text{ km}}{8 \text{ km/h}} $ $ \text{Time} = 3 \text{ hours} $It will take 3 hours for the faster motorcyclist to overtake the slower one.
Step 3: Calculate the Distance Travelled by the Faster Motorcyclist
To find how far the faster motorcyclist travels, multiply their speed by the time taken to overtake:
$ \text{Distance} = S_{fast} \times \text{Time} $ $ \text{Distance} = 20 \text{ km/h} \times 3 \text{ hours} $ $ \text{Distance} = 60 \text{ km} $The faster motorcyclist travels 60 km to overtake the slower motorcyclist.
Similar Questions
Ajay and Vijay start from the same point and walk at 4 km/h and 5 km/h respectively, in the same direction.
What will be the distance between them after 2 hours?
- A thief and a police officer are 500 meters apart. If they run in the same direction, the police officer catches the thief in 10 minutes. If they run towards each other, they meet in 2 minutes. What is the speed of the thief in meters per minute?
Important Questions from Relative Speed
In a circular race of 2500 m, a man and a woman start from a point towards opposite directions with speeds of 37 km/h and 35 km/h, respectively. After how much time from the start of the race will they meet for the first time?
- X and Yrun a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?
A train of length 600 meters passes another train of length 1000 meters moving in the opposite direction in 96 seconds. If the speed of both the trains is the same, then what is the speed of each train?
The distance between Delhi and Patna is $480$ km. A train starts from Delhi and travels towards Patna at a speed of $60$ kmph. Another train starts from Patna towards Delhi at a speed of $80$ kmph, but starts $1$ hour after the first train. In how much time, after the first train started, will they meet each other?
Ram traveling at the speed of 3 km/h reaches 15 minutes late. Had he walked at 4 km/h, he would have reached 15 minutes earlier. How much distance does Ram have to cover?
