Naresh covered 10 km 750 m by car and then walked a distance of 6 km 850 m. Find the total distance travelled by Naresh. From a rope of length 85 m 15 cm, a piece of length 47 m 95... Naresh covered 10 km 750 m by car and then walked a distance of 6 km 850 m. Find the total distance travelled by Naresh. From a rope of length 85 m 15 cm, a piece of length 47 m 95 cm is cut off. Find the length of the remaining rope.
Understand the Problem
The question consists of two parts: the first part asks to find the total distance Naresh traveled after covering a distance by car and walking. The second part requires calculating the remaining length of a rope after a piece has been cut off. The approach involves adding and subtracting distances, respectively.
Answer
The total distance traveled by Naresh is $17,600 \, \text{m}$ and the remaining length of the rope is $37.20 \, \text{m}$.
Answer for screen readers
Total distance traveled by Naresh is $17,600 , \text{m}$ and the remaining length of the rope is $37.20 , \text{m}$.
Steps to Solve
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Convert Distances to a Consistent Unit (Part 1)
For the first part, convert all distances to meters to make calculations easier.
- Car distance: $10 , \text{km} , 750 , \text{m} = 10,000 , \text{m} + 750 , \text{m} = 10,750 , \text{m}$
- Walking distance: $6 , \text{km} , 850 , \text{m} = 6,000 , \text{m} + 850 , \text{m} = 6,850 , \text{m}$
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Calculate Total Distance (Part 1)
Add the distances traveled by car and by walking:
$$ \text{Total Distance} = 10,750 , \text{m} + 6,850 , \text{m} $$
Calculate:
$$ = 17,600 , \text{m} $$
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Convert Distances for the Rope (Part 2)
For the second part, convert the lengths of the rope and the cut piece to the same unit. Keep the rope length in meters and convert the cut length from centimeters to meters:
- Rope length: $85 , \text{m} , 15 , \text{cm} = 85.15 , \text{m}$
- Piece cut: $47 , \text{m} , 95 , \text{cm} = 47.95 , \text{m}$
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Calculate Remaining Rope Length (Part 2)
Subtract the length of the cut piece from the original rope length:
$$ \text{Remaining Rope} = 85.15 , \text{m} - 47.95 , \text{m} $$
Calculate:
$$ = 37.20 , \text{m} $$
Total distance traveled by Naresh is $17,600 , \text{m}$ and the remaining length of the rope is $37.20 , \text{m}$.
More Information
- Naresh traveled a total of 17.6 kilometers, combining his car ride and walk.
- After cutting the rope, a remainder of 37.2 meters shows the importance of precision in length measurements.
Tips
- Confusing kilometers with meters. Always ensure to convert distances to the same unit before performing calculations.
- Not handling the conversion of centimeters to meters correctly. Remember that $100 , \text{cm} = 1 , \text{m}$.
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