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A man covers 1/3rd of his journey by cycle at 50 km/ h, the next 1/3 by car at 30 km/h, and the rest by walking at 7 km/h. Find the average speed during the whole journey.
- a)14.2 kmph
- b)15.29 kmph
- c)18.2 kmph
- d)12.8 kmph
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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A man covers 1/3rd of his journey by cycle at 50 km/ h, the next 1/3 b...
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A man covers 1/3rd of his journey by cycle at 50 km/ h, the next 1/3 b...
Let's assume the total distance of the journey is D km.
Coverage by Cycle:
The man covers 1/3rd of the journey by cycle at a speed of 50 km/h. So, the distance covered by cycle is (1/3)D km. The time taken to cover this distance can be calculated using the formula:
Time = Distance / Speed
Time taken by cycle = ((1/3)D) / 50 = (D / 150) hours
Coverage by Car:
The man covers the next 1/3rd of the journey by car at a speed of 30 km/h. So, the distance covered by car is also (1/3)D km. The time taken to cover this distance can be calculated using the same formula:
Time taken by car = ((1/3)D) / 30 = (D / 90) hours
Coverage by Walking:
The man covers the remaining distance by walking at a speed of 7 km/h. The distance covered by walking can be calculated as:
Distance covered by walking = D - ((1/3)D + (1/3)D) = D - (2/3)D = (1/3)D km
The time taken to cover this distance can be calculated using the formula:
Time taken by walking = ((1/3)D) / 7 = (D / 21) hours
Total Time and Average Speed:
The total time taken for the entire journey is the sum of the times taken for each mode of transport:
Total Time = Time taken by cycle + Time taken by car + Time taken by walking
Total Time = (D / 150) + (D / 90) + (D / 21)
The average speed during the whole journey can be calculated using the formula:
Average Speed = Total Distance / Total Time
Average Speed = D / (Total Time)
Now, substitute the values of Total Time and simplify the expression to find the average speed:
Average Speed = D / [(D / 150) + (D / 90) + (D / 21)]
To simplify the expression, we can find the least common multiple (LCM) of 150, 90, and 21, which is 630.
Average Speed = D / [(D * 630 / 150) + (D * 630 / 90) + (D * 630 / 21)]
Average Speed = D / [(21 * D) + (7 * D) + (30 * D)] / 630
Average Speed = D / (58 * D) / 630
Average Speed = 630 / 58
Average Speed = 10.86 km/h
The correct answer is option 'B' - 15.29 km/h.
Coverage by Cycle:
The man covers 1/3rd of the journey by cycle at a speed of 50 km/h. So, the distance covered by cycle is (1/3)D km. The time taken to cover this distance can be calculated using the formula:
Time = Distance / Speed
Time taken by cycle = ((1/3)D) / 50 = (D / 150) hours
Coverage by Car:
The man covers the next 1/3rd of the journey by car at a speed of 30 km/h. So, the distance covered by car is also (1/3)D km. The time taken to cover this distance can be calculated using the same formula:
Time taken by car = ((1/3)D) / 30 = (D / 90) hours
Coverage by Walking:
The man covers the remaining distance by walking at a speed of 7 km/h. The distance covered by walking can be calculated as:
Distance covered by walking = D - ((1/3)D + (1/3)D) = D - (2/3)D = (1/3)D km
The time taken to cover this distance can be calculated using the formula:
Time taken by walking = ((1/3)D) / 7 = (D / 21) hours
Total Time and Average Speed:
The total time taken for the entire journey is the sum of the times taken for each mode of transport:
Total Time = Time taken by cycle + Time taken by car + Time taken by walking
Total Time = (D / 150) + (D / 90) + (D / 21)
The average speed during the whole journey can be calculated using the formula:
Average Speed = Total Distance / Total Time
Average Speed = D / (Total Time)
Now, substitute the values of Total Time and simplify the expression to find the average speed:
Average Speed = D / [(D / 150) + (D / 90) + (D / 21)]
To simplify the expression, we can find the least common multiple (LCM) of 150, 90, and 21, which is 630.
Average Speed = D / [(D * 630 / 150) + (D * 630 / 90) + (D * 630 / 21)]
Average Speed = D / [(21 * D) + (7 * D) + (30 * D)] / 630
Average Speed = D / (58 * D) / 630
Average Speed = 630 / 58
Average Speed = 10.86 km/h
The correct answer is option 'B' - 15.29 km/h.
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