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
- 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?
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?
Important Questions from Relative Speed
The driver of a car, which is travelling at a speed of 75 km/h, locates a bus 80 m ahead of him, travelling in the same direction. After 15 seconds, he finds that the bus is 40 m behind the car. What is the speed of the bus (in km/h)?
The distance between two station A and B is 800 km. A train X starts from A and moves towards B at 40 km/h and another trains Y starts from B and moves towards A at 60 km/h. how far from A will they cross each other?
A and B are travelling towards each other from the points P and Q respectively. After crossing each other, A and B take \(6\frac{1}{8}\) hours and 8 hours, respectively, to reach their destinations Q and P, respectively. If the speed of B is 16.8 km/h, then the speed (in km/hr) of A is:
A train leaves station A at 8 am and reaches station B at 12 noon. A car leaves station B at 8:30 am and reaches station A at the same time when the train reaches station B. At what time do they meet?
A and B start moving towards each other from places X and Y respectively, at the same time. The speed of A is 20% more than that of B. After meeting on the way, A and B take \(2\frac{1}{2}\) hours and x hours now to reach Y and X respectively. What is the value of x?
