Two trains started at 7AM from the same point. The first train travelled north at a speed of 80km/h and the second train travelled south at a speed of 100 km/h. The time at which they were 540 km apart is _______________ AM.
Problem Analysis:
- Two trains start simultaneously from the same point.
- Train 1 travels North at 80 km/h.
- Train 2 travels South at 100 km/h.
- We need to find the time when they are 540 km apart.
- Since they travel in opposite directions (North and South), their speeds add up to determine the rate at which the distance between them increases.
Calculating Relative Speed
The relative speed is the sum of the speeds of the two trains because they are moving in opposite directions.
Relative Speed $= \text{Speed}_1 + \text{Speed}_2$
Relative Speed $= 80 \text{ km/h} + 100 \text{ km/h} = 180 \text{ km/h}$
Calculating Time Taken
The time it takes for the trains to be 540 km apart can be calculated using the formula: Time = Distance / Speed.
Time $= \frac{\text{Total Distance}}{\text{Relative Speed}}$
Time $= \frac{540 \text{ km}}{180 \text{ km/h}} = 3 \text{ hours}$
Determining Final Time
The trains started at 7 AM. They will be 540 km apart after 3 hours.
Final Time = Start Time + Time Taken
Final Time $= 7 \text{ AM} + 3 \text{ hours} = 10 \text{ AM}$
Important Questions from Speed Distance and Time
- Two cars, P and Q, start from a point X in India at 10 AM. Car P travels North with a speed of 25 km/h and car Q travels East with a speed of 30 km/h. Car P travels continuously but car Q stops for some time after travelling for one hour. If both the cars are at the same distance from X at 11:30 AM, for how long (in minutes) did car Q stop?
In a 500 m race, P and Q have speeds in the ratio of 3: 4. Q starts the race when P has already covered 140 m.
What is the distance between P and Q (in m) when P wins the race?A vehicle is moving at a speed of 12 m/s on a level road. It applies emergency brakes and starts to skid without rolling in a straight path. The deceleration of the vehicle is constant after braking and it comes to rest at a distance of 15 m. Assuming, $g = 10$ m/s$^2$, the coefficient of kinetic friction between the tyres and road is _________ [round off to 2 decimal places]
- The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?
- From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?
