To find the length of the second train, we can use the concept of relative speed and the formula for relative motion. Given two trains moving in the same direction, their relative speed is the difference in their speeds.
- First, convert the speeds from km/h to m/s, because the length of the trains are given in meters and the time in seconds.
- The first train's speed: 40 \ \text{km/h} = 40 \times \frac{1000}{3600} \ \text{m/s} = \frac{100}{9} \ \text{m/s}.
- The second train's speed: 22 \ \text{km/h} = 22 \times \frac{1000}{3600} \ \text{m/s} = \frac{55}{9} \ \text{m/s}.
- Calculate the relative speed:
- The relative speed when both are moving in the same direction is: \left(\frac{100}{9} - \frac{55}{9}\right) \ \text{m/s} = \frac{45}{9} \ \text{m/s} = 5 \ \text{m/s}.
- According to the problem, the trains take 1 minute to cross each other completely, which is 60 seconds.
- The total distance covered relatively in these 60 seconds at 5 m/s is:
- \text{Distance} = \text{Relative speed} \times \text{Time} = 5 \times 60 = 300 \ \text{meters}.
- The total length of both trains combined is 300 meters according to the distance calculation.
- Given the length of the first train is 125 meters, the length of the second train can be calculated as:
- \text{Length of second train} = 300 - 125 = 175 \ \text{meters}.
Thus, the length of the second train is 175 meters.
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Important Questions from Speed Time and Distance
A train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is
Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.
Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
A worker covers a distance of 81 km in 11 hours. He travels partly on foot at 4.5 km/h and partly on bicycle at 15 km/h. What is the distance covered on the cycle?
A car travels from a place X to place Y at an average speed of v km/hr from y to X at an average speed of 2v km/hr, again from X to y at an average speed of 3v km/hr and again from y to x at an average speed of 4v km/hr. Then the average speed of the car for the entire journey
