A train starts moving from a place A at 10:00 a.m. and arrives at another place B at 5:30 p.m. on the same day. If the speed of the train is 80 km/hr, then what will be the distance covered by the train?
600 km
Understanding the Train Journey Problem
This problem involves calculating the distance covered by a train given its speed and the duration of its journey. To solve this, we need to first determine the total time the train was travelling and then use the fundamental relationship between distance, speed, and time.
Calculating the Travel Time of the Train
The train starts its journey from place A at 10:00 a.m. and reaches place B at 5:30 p.m. on the same day. To find the total travel time, we can break down the duration:
- Time from 10:00 a.m. to 12:00 p.m. (noon) is 2 hours.
- Time from 12:00 p.m. to 5:30 p.m. is 5 hours and 30 minutes.
Adding these durations gives the total travel time:
Total Time = 2 hours + 5 hours 30 minutes = 7 hours 30 minutes.
To use this time in the distance formula, it's best to convert it entirely into hours.
30 minutes is equal to $\frac{30}{60}$ hours, which simplifies to $\frac{1}{2}$ or 0.5 hours.
So, the total travel time in hours is $7 + 0.5 = 7.5$ hours.
Applying the Distance Formula
The relationship between distance, speed, and time is given by the formula:
$\text{Distance} = \text{Speed} \times \text{Time}$
In this problem, we are given:
- Speed of the train = 80 km/hr
- Total travel time = 7.5 hours
Now, we can substitute these values into the distance formula to find the distance covered by the train.
Calculating the Distance Covered by the Train
Using the formula $\text{Distance} = \text{Speed} \times \text{Time}$:
Distance = 80 km/hr $\times$ 7.5 hours
Distance = $80 \times 7.5$ km
To calculate $80 \times 7.5$, we can write 7.5 as $\frac{15}{2}$:
Distance = $80 \times \frac{15}{2}$ km
We can cancel out the 2 with 80:
Distance = $40 \times 15$ km
Performing the multiplication:
Distance = 600 km
Thus, the distance covered by the train is 600 km.
Summary of Calculation Steps
Here is a brief summary of the steps taken to find the distance:
- Determine the start and end times of the journey.
- Calculate the total duration of the journey.
- Convert the total duration into hours.
- Identify the given speed of the train.
- Use the formula: Distance = Speed $\times$ Time.
- Substitute the values and perform the calculation.
Revision Table: Speed, Distance, and Time
| Concept | Formula | Units (Common) |
|---|---|---|
| Distance | Speed $\times$ Time | Kilometers (km), Meters (m), Miles |
| Speed | $\frac{\text{Distance}}{\text{Time}}$ | km/hr, m/s, miles/hr |
| Time | $\frac{\text{Distance}}{\text{Speed}}$ | Hours (hr), Minutes (min), Seconds (s) |
Additional Information: Time Conversion for Motion Problems
In speed, distance, and time problems, it is crucial to ensure that the units are consistent. If speed is in km/hr, time must be in hours to get distance in km. If speed is in m/s, time must be in seconds to get distance in meters.
- To convert hours to minutes, multiply by 60.
- To convert minutes to hours, divide by 60.
- To convert minutes to seconds, multiply by 60.
- To convert seconds to minutes, divide by 60.
- To convert hours to seconds, multiply by 3600 (60 $\times$ 60).
- To convert seconds to hours, divide by 3600.
Consistency in units is key to solving motion problems correctly.
Important Questions from Relative Speed
The driver of a car, which is travelling at a speed of 75 km/h, locates a bus 80 m ahead of him, travelling in the same direction. After 15 seconds, he finds that the bus is 40 m behind the car. What is the speed of the bus (in km/h)?
The distance between two station A and B is 800 km. A train X starts from A and moves towards B at 40 km/h and another trains Y starts from B and moves towards A at 60 km/h. how far from A will they cross each other?
A and B are travelling towards each other from the points P and Q respectively. After crossing each other, A and B take \(6\frac{1}{8}\) hours and 8 hours, respectively, to reach their destinations Q and P, respectively. If the speed of B is 16.8 km/h, then the speed (in km/hr) of A is:
A train leaves station A at 8 am and reaches station B at 12 noon. A car leaves station B at 8:30 am and reaches station A at the same time when the train reaches station B. At what time do they meet?
A and B start moving towards each other from places X and Y respectively, at the same time. The speed of A is 20% more than that of B. After meeting on the way, A and B take \(2\frac{1}{2}\) hours and x hours now to reach Y and X respectively. What is the value of x?
