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Two trains starting from the same station and travelling in opposite directions are 227.5 km apart in 3 hours 15 min. Had they been travelling in the same direction, they would have been 32.5 km apart in the same time. Find their speeds (in kmph).
- a)30, 40
- b)20, 50
- c)35, 45
- d)10, 60
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two trains starting from the same station and travelling in opposite d...
When the trains are travelling in opposite direction, the sum of their speeds (relative speed) = (227.5/3.25) = 70 kmph
If they had been travelling in same directions, the difference of their speeds (relative speed) = (32.5/3.25) = 10 kmph
Hence, the speed of the faster train = (70 + 10)/2 = 40 kmph and the speed of the slower train = (70 - 10)/2 = 30 kmph
If they had been travelling in same directions, the difference of their speeds (relative speed) = (32.5/3.25) = 10 kmph
Hence, the speed of the faster train = (70 + 10)/2 = 40 kmph and the speed of the slower train = (70 - 10)/2 = 30 kmph
Most Upvoted Answer
Two trains starting from the same station and travelling in opposite d...
Given:
Two trains starting from the same station and travelling in opposite directions are 227.5 km apart in 3 hours 15 min (or 3.25 hours).
If they had been travelling in the same direction, they would have been 32.5 km apart in the same time.
To find:
The speeds of the two trains in kmph.
Assumption:
Let the speed of the first train be x kmph and the speed of the second train be y kmph.
Steps to solve the problem:
1. Convert the time given in hours and minutes to hours.
3 hours 15 minutes = 3 + 15/60 = 3.25 hours.
2. Use the formula: Distance = Speed x Time to calculate the distance travelled by each train.
Distance travelled by the first train = x * 3.25 km
Distance travelled by the second train = y * 3.25 km
3. According to the problem, when the trains are travelling in opposite directions, their total distance is 227.5 km.
So, we have the equation: x * 3.25 + y * 3.25 = 227.5
4. According to the problem, when the trains are travelling in the same direction, their relative distance is 32.5 km.
So, we have the equation: x * 3.25 - y * 3.25 = 32.5
5. Solve the two equations simultaneously to find the values of x and y.
Multiplying the second equation by -1, we get: -x * 3.25 + y * 3.25 = -32.5
Adding the two equations, we get:
(x * 3.25 + y * 3.25) + (-x * 3.25 + y * 3.25) = 227.5 + (-32.5)
Simplifying the equation, we get: 2y * 3.25 = 195
Dividing both sides of the equation by 2 * 3.25, we get: y = 30
Substituting the value of y in any of the equations, we get: x = 40
6. Therefore, the speeds of the two trains are 40 kmph and 30 kmph respectively.
Hence, the correct answer is option 'A' - 30 and 40.
Two trains starting from the same station and travelling in opposite directions are 227.5 km apart in 3 hours 15 min (or 3.25 hours).
If they had been travelling in the same direction, they would have been 32.5 km apart in the same time.
To find:
The speeds of the two trains in kmph.
Assumption:
Let the speed of the first train be x kmph and the speed of the second train be y kmph.
Steps to solve the problem:
1. Convert the time given in hours and minutes to hours.
3 hours 15 minutes = 3 + 15/60 = 3.25 hours.
2. Use the formula: Distance = Speed x Time to calculate the distance travelled by each train.
Distance travelled by the first train = x * 3.25 km
Distance travelled by the second train = y * 3.25 km
3. According to the problem, when the trains are travelling in opposite directions, their total distance is 227.5 km.
So, we have the equation: x * 3.25 + y * 3.25 = 227.5
4. According to the problem, when the trains are travelling in the same direction, their relative distance is 32.5 km.
So, we have the equation: x * 3.25 - y * 3.25 = 32.5
5. Solve the two equations simultaneously to find the values of x and y.
Multiplying the second equation by -1, we get: -x * 3.25 + y * 3.25 = -32.5
Adding the two equations, we get:
(x * 3.25 + y * 3.25) + (-x * 3.25 + y * 3.25) = 227.5 + (-32.5)
Simplifying the equation, we get: 2y * 3.25 = 195
Dividing both sides of the equation by 2 * 3.25, we get: y = 30
Substituting the value of y in any of the equations, we get: x = 40
6. Therefore, the speeds of the two trains are 40 kmph and 30 kmph respectively.
Hence, the correct answer is option 'A' - 30 and 40.
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Two trains starting from the same station and travelling in opposite directions are 227.5 km apart in 3 hours 15 min. Had they been travelling in the same direction, they would have been 32.5 km apart in the same time. Find their speeds (in kmph).a)30, 40b)20, 50c)35, 45d)10, 60Correct answer is option 'A'. Can you explain this answer?
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