Calculating Train Travel Time
This solution explains how to find the time taken for a train to cover a specific distance at a given speed.
Step 1: Convert Speed Units
The distance is given in kilometers (km), but the speed is in meters per second (m/s). To use the standard formula relating distance, speed, and time, we need consistent units. We will convert the speed from m/s to kilometers per hour (km/h).
- The conversion factor from m/s to km/h is $\frac{18}{5}$.
- Given speed = $20$ m/s.
- Speed in km/h = $20 \times \frac{18}{5}$ km/h.
- Speed = $4 \times 18$ km/h = $72$ km/h.
Step 2: Calculate Time Taken
The relationship between distance ($d$), speed ($v$), and time ($t$) is given by the formula:
$ t = \frac{d}{v} $
- Distance ($d$) = $360$ km.
- Speed ($v$) = $72$ km/h.
- Time ($t$) = $\frac{360 \text{ km}}{72 \text{ km/h}}$.
- Time ($t$) = $5$ hours.
Therefore, the time taken to cover the distance is 5 hours.
Important Questions from Speed Time and Distance
- Daksh travels 200 km at 50 km/hr, the next 252 km at 42 km/hr and the next 204 km at 51 km/hr. What is his average speed (in km/hr) for the whole journey? (Round off your answer to two decimal places)
- A bus travelling at 66 km/hr completes a journey in 15 hours. What should be its speed to cover the same distance in 5 hours?
- Train A leaves station M at 8:00 a.m. and reaches station N at 3:00 p.m. on the same day. Train B leaves station N at 10:00 a.m. and reaches station M at 3:00 p.m. on the same day. Find the time when Trains A and B meet.
- A bus travelling at 95 km/hr completes a journey in 10 hours. What should be in its speed to cover the same distance in 5 hours?
Rishi travels 198 km at 66 km/hr, the next 584 km at 73 km/hr and the next 656 km at 82 km/hr. What is his average speed (in km/hr) for the whole journey? (Round off your answer to two decimal places)
