Sravan drove from home to a neighbouring town at a speed of 50 km/h. On his return journey he drove at 45 km/h and took 1 hour longer to reach home. What distance (in km) did he cover one way?

Introduction / Context:
This is a classic time, speed, and distance problem in which the distances are the same in both directions but speeds differ, causing different travel times. The key idea is to express both times in terms of distance and use the given difference in time to solve for the distance.

Given Data / Assumptions:
- Speed from home to town = 50 km/h. - Speed from town back to home = 45 km/h. - Return journey takes 1 hour longer than the onward journey. - Let one way distance be d km. - Distances going and coming back are equal.

Concept / Approach:
Time equals distance divided by speed. Let t1 be the time from home to town and t2 be the time from town to home. Then t1 = d / 50 and t2 = d / 45. According to the problem, t2 is 1 hour longer than t1, so t2 - t1 = 1. This equation in d can be solved using simple fraction manipulation to obtain the distance.

Step-by-Step Solution:
Step 1: Time for onward journey: t1 = d / 50 hours. Step 2: Time for return journey: t2 = d / 45 hours. Step 3: Given that t2 = t1 + 1. Step 4: So d / 45 = d / 50 + 1. Step 5: Bring terms together: d / 45 - d / 50 = 1. Step 6: Use common denominator 2250: (50d - 45d) / 2250 = 1. Step 7: This gives 5d / 2250 = 1. Step 8: Multiply both sides by 2250 to get 5d = 2250. Step 9: Therefore d = 2250 / 5 = 450 km.

Verification / Alternative check:
If d = 450 km, onward time t1 = 450 / 50 = 9 hours. Return time t2 = 450 / 45 = 10 hours. Difference t2 - t1 = 10 - 9 = 1 hour, which matches the given condition. Therefore, 450 km is consistent with the problem statement.

Why Other Options Are Wrong:
- 350 km or 500 km would lead to time differences smaller or larger than 1 hour. - 700 km and 900 km give onward and return times whose differences do not match the required 1 hour. - Only 450 km satisfies the exact time difference required.

Common Pitfalls:
A typical mistake is to set up the equation as t1 - t2 = 1 instead of t2 - t1 = 1 or to average the two speeds incorrectly. Another error is to forget that the distance both ways is the same. Always start with d / speed expressions for each leg and carefully follow the condition about which time is longer.

Final Answer:
Sravan covered a one way distance of 450 km.