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
- A car is moving on a horizontal surface in a straight line with a constant velocity of 3 m/s. A ball is thrown vertically upwards at time $t = 0$ from the top of the moving car with a velocity of 20 m/s. The acceleration due to gravity is 10 m/s$^2$.
At what value(s) of time $t$ in second(s), the ball is at a height of 15 m from the top of the moving car? - Velocity of an object fired directly in upward direction is given by $V = 80 – 32 \ t$, where $t$ (time) is in seconds. When will the velocity be between 32 m/sec and 64 m/sec?
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?- An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey?
Two cars start at the same time from the same location and go in the same direction. The speed of the first car is 50 km/h and the speed of the second car is 60 km/h. The number of hours it takes for the distance between the two cars to be 20 km is ___________.
