Calculating Bus Meeting Time
This problem involves calculating the time it takes for two objects moving towards each other to meet. We are given the total distance separating them and their individual speeds.
Finding Relative Speed
When two objects move towards each other, their speeds add up to determine how quickly the distance between them closes. This is called their relative speed.
- Speed of Bus 1: \( v_1 = 20 \) km/hr
- Speed of Bus 2: \( v_2 = 18 \) km/hr
- Relative Speed: \( v_{rel} = v_1 + v_2 \)
Calculating the relative speed:
\( v_{rel} = 20 \text{ km/hr} + 18 \text{ km/hr} = 38 \text{ km/hr} \)
Calculating Time to Meet
The time it takes for the buses to meet is found by dividing the total distance between them by their relative speed.
- Distance: \( d = 76 \) km
- Relative Speed: \( v_{rel} = 38 \) km/hr
- Time = Distance / Relative Speed
Calculating the time:
\( t = \frac{d}{v_{rel}} = \frac{76 \text{ km}}{38 \text{ km/hr}} \)
\( t = 2 \) hours
Therefore, the buses will meet each other after 2 hours.
Important Questions from Partial Speed
- A motorboat moves along a straight line path along a river bank from point A to point B. If the speed of the boat in still water is doubled, then the trip from A to B and back again would take 20% of the time that the motorboat usually takes for the journey. By how many times is the actual speed of the motorboat higher than the speed of the river flow?
- Walking at $\frac{3}{4}$ of his usual speed, a man is $1\frac{1}{2}$ hours late. His usual time to cover the same distance (in hours) is-
- Two busses are at two different places 76 km apart. They start moving towards each other. If their speeds are 20 km/hr and 18 km/hr respectively, after how much time will they meet each other?
- A man covers distance of 1400 km in 80 days resting 10 hours a day. If he rests 16 hours a day and walks at 2.5 times the previous speed, then in how many days will he cover 1000 km?
- A man covers distance of 1400km in 80 days resting 10 hours a day. If he rests 16 hours a day and walks at 2.5 times the previous speed, then in how many days will he cover 1000 km?
