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
In a circular race of 2500 m, a man and a woman start from a point towards opposite directions with speeds of 37 km/h and 35 km/h, respectively. After how much time from the start of the race will they meet for the first time?
- X and Yrun a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?
A train of length 600 meters passes another train of length 1000 meters moving in the opposite direction in 96 seconds. If the speed of both the trains is the same, then what is the speed of each train?
The distance between Delhi and Patna is $480$ km. A train starts from Delhi and travels towards Patna at a speed of $60$ kmph. Another train starts from Patna towards Delhi at a speed of $80$ kmph, but starts $1$ hour after the first train. In how much time, after the first train started, will they meet each other?
Ram traveling at the speed of 3 km/h reaches 15 minutes late. Had he walked at 4 km/h, he would have reached 15 minutes earlier. How much distance does Ram have to cover?
