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The train A left Delhi at noon sharp. Four hours later, another train B started from Delhi in the same direction. The train B overtook the train A at 10 p.m. Find the average speed of the both trains over this journey if the sum of their speed is 80 km/h.
- a)40 km/h
- b)50 km/h
- c)37.5 km/h
- d)36km/h
Correct answer is option 'C'. Can you explain this answer?
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The train A left Delhi at noon sharp. Four hours later, another train ...
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The train A left Delhi at noon sharp. Four hours later, another train ...
To find the average speed of both trains over the journey, we need to determine the individual speeds of Train A and Train B.
Let's assume the speed of Train A is x km/h and the speed of Train B is y km/h.
Given that the sum of their speeds is 80 km/h, we can write the equation:
x + y = 80
We also know that Train B started four hours later than Train A and overtook it at 10 p.m. This means that Train B traveled for 10 - 4 = 6 hours.
- First Step: Determining the Distance Traveled by Train A
To find the distance traveled by Train A, we need to calculate the time it took for Train B to overtake Train A. Since Train B started four hours after Train A and overtook it after 10 hours, Train A traveled for 10 + 4 = 14 hours.
- Second Step: Determining the Distance Traveled by Train B
Train B traveled for 6 hours, as mentioned earlier.
- Third Step: Using the Formula to Calculate Speed
The formula to calculate speed is:
Speed = Distance / Time
- Fourth Step: Applying the Formula to Both Trains
Using the formula, we can calculate the speeds of both trains as follows:
Speed of Train A = Distance traveled by Train A / Time taken by Train A = Distance traveled by Train A / 14 hours
Speed of Train B = Distance traveled by Train B / Time taken by Train B = Distance traveled by Train B / 6 hours
- Fifth Step: Substituting Known Values and Solving the Equations
We know that Train A and Train B traveled the same distance, so their distances are equal. Therefore, we can equate the distances traveled by both trains:
Distance traveled by Train A = Distance traveled by Train B
Distance traveled by Train A / 14 hours = Distance traveled by Train B / 6 hours
Since the distances are equal, we can equate the two equations:
Distance traveled by Train A / 14 = Distance traveled by Train B / 6
Simplifying the equation, we get:
6 * Distance traveled by Train A = 14 * Distance traveled by Train B
Dividing both sides of the equation by Distance traveled by Train B, we get:
6 / 14 = Distance traveled by Train A / Distance traveled by Train B
Simplifying further, we find:
3 / 7 = Distance traveled by Train A / Distance traveled by Train B
Since the ratio of the distances traveled by Train A and Train B is equal to the ratio of their speeds, we can substitute the speeds into the equation:
3 / 7 = Speed of Train A / Speed of Train B
We know that the sum of their speeds is 80 km/h:
Speed of Train A + Speed of Train B = 80
Substituting the value of Speed of Train A from the earlier equation, we get:
3 / 7 = (80 - Speed of Train B) / Speed of Train B
Simplifying the equation, we get:
3 * Speed of Train B = 7 * (80 - Speed of Train B)
Expanding the equation, we get:
3 * Speed of Train B = 560 - 7 * Speed of Train B
Combining like terms, we get:
10 * Speed of Train B = 560
Dividing both sides
Let's assume the speed of Train A is x km/h and the speed of Train B is y km/h.
Given that the sum of their speeds is 80 km/h, we can write the equation:
x + y = 80
We also know that Train B started four hours later than Train A and overtook it at 10 p.m. This means that Train B traveled for 10 - 4 = 6 hours.
- First Step: Determining the Distance Traveled by Train A
To find the distance traveled by Train A, we need to calculate the time it took for Train B to overtake Train A. Since Train B started four hours after Train A and overtook it after 10 hours, Train A traveled for 10 + 4 = 14 hours.
- Second Step: Determining the Distance Traveled by Train B
Train B traveled for 6 hours, as mentioned earlier.
- Third Step: Using the Formula to Calculate Speed
The formula to calculate speed is:
Speed = Distance / Time
- Fourth Step: Applying the Formula to Both Trains
Using the formula, we can calculate the speeds of both trains as follows:
Speed of Train A = Distance traveled by Train A / Time taken by Train A = Distance traveled by Train A / 14 hours
Speed of Train B = Distance traveled by Train B / Time taken by Train B = Distance traveled by Train B / 6 hours
- Fifth Step: Substituting Known Values and Solving the Equations
We know that Train A and Train B traveled the same distance, so their distances are equal. Therefore, we can equate the distances traveled by both trains:
Distance traveled by Train A = Distance traveled by Train B
Distance traveled by Train A / 14 hours = Distance traveled by Train B / 6 hours
Since the distances are equal, we can equate the two equations:
Distance traveled by Train A / 14 = Distance traveled by Train B / 6
Simplifying the equation, we get:
6 * Distance traveled by Train A = 14 * Distance traveled by Train B
Dividing both sides of the equation by Distance traveled by Train B, we get:
6 / 14 = Distance traveled by Train A / Distance traveled by Train B
Simplifying further, we find:
3 / 7 = Distance traveled by Train A / Distance traveled by Train B
Since the ratio of the distances traveled by Train A and Train B is equal to the ratio of their speeds, we can substitute the speeds into the equation:
3 / 7 = Speed of Train A / Speed of Train B
We know that the sum of their speeds is 80 km/h:
Speed of Train A + Speed of Train B = 80
Substituting the value of Speed of Train A from the earlier equation, we get:
3 / 7 = (80 - Speed of Train B) / Speed of Train B
Simplifying the equation, we get:
3 * Speed of Train B = 7 * (80 - Speed of Train B)
Expanding the equation, we get:
3 * Speed of Train B = 560 - 7 * Speed of Train B
Combining like terms, we get:
10 * Speed of Train B = 560
Dividing both sides
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The train A left Delhi at noon sharp. Four hours later, another train B started from Delhi in the same direction. The train B overtook the train A at 10 p.m. Find the average speed of the both trains over this journey if the sum of their speed is 80 km/h.a)40 km/hb)50 km/hc)37.5 km/hd)36km/hCorrect answer is option 'C'. Can you explain this answer?
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The train A left Delhi at noon sharp. Four hours later, another train B started from Delhi in the same direction. The train B overtook the train A at 10 p.m. Find the average speed of the both trains over this journey if the sum of their speed is 80 km/h.a)40 km/hb)50 km/hc)37.5 km/hd)36km/hCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The train A left Delhi at noon sharp. Four hours later, another train B started from Delhi in the same direction. The train B overtook the train A at 10 p.m. Find the average speed of the both trains over this journey if the sum of their speed is 80 km/h.a)40 km/hb)50 km/hc)37.5 km/hd)36km/hCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The train A left Delhi at noon sharp. Four hours later, another train B started from Delhi in the same direction. The train B overtook the train A at 10 p.m. Find the average speed of the both trains over this journey if the sum of their speed is 80 km/h.a)40 km/hb)50 km/hc)37.5 km/hd)36km/hCorrect answer is option 'C'. Can you explain this answer?.
The train A left Delhi at noon sharp. Four hours later, another train B started from Delhi in the same direction. The train B overtook the train A at 10 p.m. Find the average speed of the both trains over this journey if the sum of their speed is 80 km/h.a)40 km/hb)50 km/hc)37.5 km/hd)36km/hCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The train A left Delhi at noon sharp. Four hours later, another train B started from Delhi in the same direction. The train B overtook the train A at 10 p.m. Find the average speed of the both trains over this journey if the sum of their speed is 80 km/h.a)40 km/hb)50 km/hc)37.5 km/hd)36km/hCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The train A left Delhi at noon sharp. Four hours later, another train B started from Delhi in the same direction. The train B overtook the train A at 10 p.m. Find the average speed of the both trains over this journey if the sum of their speed is 80 km/h.a)40 km/hb)50 km/hc)37.5 km/hd)36km/hCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The train A left Delhi at noon sharp. Four hours later, another train B started from Delhi in the same direction. The train B overtook the train A at 10 p.m. Find the average speed of the both trains over this journey if the sum of their speed is 80 km/h.a)40 km/hb)50 km/hc)37.5 km/hd)36km/hCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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