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?
Calculating Distance Between Ajay and Vijay
This problem involves finding the separation distance between two individuals, Ajay and Vijay, after a specific time, given their different speeds but the same starting point and direction.
Understanding Relative Speed
When two objects move in the same direction, their relative speed is the difference between their individual speeds. This relative speed tells us how quickly the distance between them is changing.
- Ajay's speed ($s_A$) = 4 km/h
- Vijay's speed ($s_V$) = 5 km/h
- Time ($t$) = 2 hours
Calculating Relative Speed and Distance
First, find the relative speed of Vijay with respect to Ajay:
Relative speed ($s_{rel}$) = Vijay's speed - Ajay's speed
$s_{rel} = s_V - s_A$ $s_{rel} = 5 \text{ km/h} - 4 \text{ km/h}$ $s_{rel} = 1 \text{ km/h}$This means Vijay gains 1 km on Ajay every hour.
Now, calculate the distance between them after 2 hours using the formula: Distance = Relative Speed × Time
$d = s_{rel} \times t$ $d = 1 \text{ km/h} \times 2 \text{ h}$ $d = 2 \text{ km}$Alternative Method: Individual Distances
Alternatively, we can calculate the distance each person covers individually and then find the difference.
- Distance covered by Ajay ($d_A$) = Ajay's speed × Time = $4 \text{ km/h} \times 2 \text{ h} = 8 \text{ km}$
- Distance covered by Vijay ($d_V$) = Vijay's speed × Time = $5 \text{ km/h} \times 2 \text{ h} = 10 \text{ km}$
The distance between them is the difference between the distances they covered:
$d = d_V - d_A$ $d = 10 \text{ km} - 8 \text{ km}$ $d = 2 \text{ km}$Both methods confirm that the distance between Ajay and Vijay after 2 hours is 2 km.
Similar Questions
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- The speeds of two motorcyclists are in the ratio 5 : 3. If the slower motorcyclist has a 24 km head start, and his speed is 12 km/h, how far (in km) will the faster motorcyclist travel to overtake him?
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?
