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
Amit travelled a distance of 50 km in 9 hours. He travelled partly on foot at 5 km/h and partly by bicycle at 10 km/h. The distance travelled on the bicycle is:
Walking at 3/5 of his usual speed, a person reaches his office 20 minute later than the usual time. His usual time in minutes is:
Walking at 7/9 of his usual speed, a person reaches his office 10 minutes later than the usual time. His usual time in minutes is:
A man travelled a distance of 42 km in 5 hours. He travelled partly on foot at the rate of 6 km/h and partly on bicycle at the rate of 10 km/h. The distance travelled on foot is:
A train takes \(2\frac{1}{2}\) hours less for a journey of 300 km, if its speed is increased by 20 km/h from its usual speed. How much time will it take to cover a distance of 192 km at its usual speed?
