On Monday, Akash ran 4 km less than the distance he ran on Tuesday. Sanjay, who ran the same distance on Monday and Tuesday, ran 5 km more on Tuesday than the distance Akash ran on Monday. Find the difference between the distance covered by Akash and Sanjay over the two days.
Show Hint
- 5 km
- 6 km
- 4 km
- 9 km
The Correct Option is B
Solution and Explanation
Let the distance Akash ran on Monday be \( x \) km. Then the distance Akash ran on Tuesday is \( x + 4 \) km (since he ran 4 km more on Tuesday).
For Sanjay, he ran the same distance on both days, and the distance on Monday is \( y \) km. On Tuesday, he ran 5 km more than Akash's distance on Monday, so the distance Sanjay ran on Tuesday is \( y + 5 \) km.
We are asked to find the difference between the total distances covered by Akash and Sanjay over the two days.
- Akash's total distance = \( x + (x + 4) = 2x + 4 \) km.
- Sanjay's total distance = \( y + (y + 5) = 2y + 5 \) km.
We know that Sanjay ran the same total distance as Akash, so: \[ 2x + 4 = 2y + 5 \] Simplifying the equation: \[ 2x - 2y = 1 \Rightarrow x - y = \frac{1}{2} \] Now, calculating the difference in their total distances: \[ \text{Difference} = |(2x + 4) - (2y + 5)| = |1 + 6| = 6 \text{ km} \] Thus, the difference between the distance covered by Akash and Sanjay over the two days is \( \boxed{6} \) km.
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