Question:
Vedant travels 60 Km per hour going to a neighboring city and 50 km per hour coming back using same road. He drive a total of 5 hours away and back. What is the distance from Vedant's house to the city.
Vedant travels 60 Km per hour going to a neighboring city and 50 km per hour coming back using same road. He drive a total of 5 hours away and back. What is the distance from Vedant's house to the city.
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To solve round-trip distance problems quickly, use the formula:
\[ \text{Distance} = \frac{v_1 \times v_2}{v_1 + v_2} \times T_{\text{total}} = \frac{60 \times 50}{60 + 50} \times 5 = \frac{3000}{110} \times 5 = \frac{1500}{11} \approx 136\text{ km}. \]
This formula simplifies the calculations significantly.
\[ \text{Distance} = \frac{v_1 \times v_2}{v_1 + v_2} \times T_{\text{total}} = \frac{60 \times 50}{60 + 50} \times 5 = \frac{3000}{110} \times 5 = \frac{1500}{11} \approx 136\text{ km}. \]
This formula simplifies the calculations significantly.
Updated On: Aug 18, 2026
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
This problem describes a round-trip journey along the same route at different speeds.
The total time taken is the sum of the time spent traveling to the destination and the time spent returning.
Using the relationships between distance, speed, and time, we can write a single variable equation to solve for the distance.
Key Formula or Approach:
The formula for time is: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \] Let the distance from Vedant's house to the neighboring city be $D\text{ km}$.
The total time equation is: \[ T_{\text{total}} = T_{\text{going}} + T_{\text{returning}} = \frac{D}{v_{\text{going}}} + \frac{D}{v_{\text{returning}}} \]
Step 2: Detailed Explanation:
Let us plug in the given values:
- Speed going to the city ($v_{\text{going}}$) $= 60\text{ km/h}$
- Speed returning ($v_{\text{returning}}$) $= 50\text{ km/h}$
- Total time ($T_{\text{total}}$) $= 5\text{ hours}$
Write the equation: \[ \frac{D}{60} + \frac{D}{50} = 5 \] To solve this equation, find a common denominator for $60$ and $50$, which is $300$: \[ \frac{5D + 6D}{300} = 5 \] \[ \frac{11D}{300} = 5 \] Multiply both sides by $300$: \[ 11D = 1500 \] Solve for $D$: \[ D = \frac{1500}{11} \approx 136\text{ km} \] Rounding to the nearest whole integer, the distance is approximately $136\text{ km}$.
Step 3: Final Answer:
The distance from Vedant's house to the neighboring city is approximately 136 km.
Therefore, the correct option is (D).
This problem describes a round-trip journey along the same route at different speeds.
The total time taken is the sum of the time spent traveling to the destination and the time spent returning.
Using the relationships between distance, speed, and time, we can write a single variable equation to solve for the distance.
Key Formula or Approach:
The formula for time is: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \] Let the distance from Vedant's house to the neighboring city be $D\text{ km}$.
The total time equation is: \[ T_{\text{total}} = T_{\text{going}} + T_{\text{returning}} = \frac{D}{v_{\text{going}}} + \frac{D}{v_{\text{returning}}} \]
Step 2: Detailed Explanation:
Let us plug in the given values:
- Speed going to the city ($v_{\text{going}}$) $= 60\text{ km/h}$
- Speed returning ($v_{\text{returning}}$) $= 50\text{ km/h}$
- Total time ($T_{\text{total}}$) $= 5\text{ hours}$
Write the equation: \[ \frac{D}{60} + \frac{D}{50} = 5 \] To solve this equation, find a common denominator for $60$ and $50$, which is $300$: \[ \frac{5D + 6D}{300} = 5 \] \[ \frac{11D}{300} = 5 \] Multiply both sides by $300$: \[ 11D = 1500 \] Solve for $D$: \[ D = \frac{1500}{11} \approx 136\text{ km} \] Rounding to the nearest whole integer, the distance is approximately $136\text{ km}$.
Step 3: Final Answer:
The distance from Vedant's house to the neighboring city is approximately 136 km.
Therefore, the correct option is (D).
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