Running Friends Meeting Time
This problem requires calculating the time it takes for two individuals moving towards each other to meet. The key concept used is relative speed.
Given Distance and Speeds
- Initial distance between the friends: $D = 10$ km
- Speed of the first friend: $S_1 = 10$ km/hr
- Speed of the second friend: $S_2 = 14$ km/hr
Relative Speed Calculation
When two objects move towards each other, their speeds combine. This combined speed, known as relative speed, determines how quickly the distance between them decreases.
Relative speed, $S_{rel} = S_1 + S_2$
$S_{rel} = 10 \text{ km/hr} + 14 \text{ km/hr} = 24 \text{ km/hr}$
Time to Meet Calculation
The time required for the friends to meet is calculated by dividing the total initial distance by their relative speed.
Time, $T = \frac{D}{S_{rel}}$
$T = \frac{10 \text{ km}}{24 \text{ km/hr}} = \frac{10}{24}$ hours
Time to Minutes Conversion
To express the meeting time in minutes, convert the time from hours by multiplying by 60.
$T_{\text{minutes}} = \frac{10}{24} \times 60$ minutes
$T_{\text{minutes}} = \frac{600}{24}$ minutes
$T_{\text{minutes}} = 25$ minutes
The calculation indicates the friends will meet in 25 minutes. Option C is 28 minutes.
Important Questions from Relative Speed
- Ankur jogs on a circular track X at $1 \frac{2}{3}$ m/s and Mahima jogs on track Y at $2 \frac{1}{12}$ m/s. The total length of Tracks X and Y is 0.325 km. Ankur makes 9 rounds of track X in the same time Mahima makes 5 rounds of track Y. The time taken (in seconds) by Mahima to complete one round of track X is:
- Two places, A and B are 3710 kms from each other. A train leaves from A to B at the same time another train leaves B to A. The two trains meet at the end of 35 hours. If the train travelling from A to B travels 35 kmph faster than the other. Find the speed of the faster train. (In kmph)
- A truck, 1575 metres long is running at a speed of 109 km/hr. How many seconds will it take to cross a 1475 metres long train running in the same direction at a speed of 79 km/hr?
- A truck, 1600 metres long is running at a speed of 112 km/hr. How many seconds will it take to cross a 1500 metres long train running in the same direction at a speed of 82 km/hr?
Consider an equilateral triangle ABC as given in the following diagram :
Two people start at the same time from points A and B with speeds 30 km per hour and 20 km per hour respectively, and move on the sides of the triangle in the clockwise direction. They meet each other for the first time at
