Meeting Time Calculation for Two Buses
This problem involves calculating the time it takes for two objects moving towards each other to meet.
Understanding Relative Speed
When two objects move towards each other, their relative speed is the sum of their individual speeds. This relative speed determines how quickly the distance between them closes.
Solution Steps
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Identify Given Information:
- Distance between buses, $D = 76 \text{ km}$
- Speed of the first bus, $S_1 = 20 \text{ km/hr}$
- Speed of the second bus, $S_2 = 18 \text{ km/hr}$
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Calculate Relative Speed:
Since the buses are moving towards each other, we add their speeds:
Relative Speed, $S_{rel} = S_1 + S_2 = 20 \text{ km/hr} + 18 \text{ km/hr} = 38 \text{ km/hr}$
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Calculate Meeting Time:
The time taken to meet is the total distance divided by the relative speed:
Time, $T = \frac{D}{S_{rel}}$
Substitute the values:
$T = \frac{76 \text{ km}}{38 \text{ km/hr}}$
$T = 2 \text{ hrs}$
Conclusion
The two 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?
