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
- 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?
- 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?
