Sravan drives from home to a neighbouring town at 50 km/h and returns at 45 km/h. The return journey takes one hour longer than the onward journey. What distance (in km) does he cover one way?

Introduction / Context:
This is a classic average speed type question on a road journey, structurally similar to boats and streams problems. Sravan drives to a town at one speed and returns at a different speed, with the return trip taking one hour longer than the outward trip. The distance one way is the same in both directions, so we can formulate an equation in terms of distance and travel times to find the unknown distance.

Given Data / Assumptions:

• Speed from home to town = 50 km/h.
• Speed from town back home = 45 km/h.
• Return trip takes 1 hour longer than the onward trip.
• Let D be the one way distance in km.
• Speeds are constant and there are no other delays.

Concept / Approach:
Time is distance divided by speed. If T1 is the time from home to town and T2 is the time back, then:

• T1 = D / 50.
• T2 = D / 45.

Given that T2 = T1 + 1, we form an equation and solve for D. This algebraic approach is straightforward and robust.

Step-by-Step Solution:
Let D be the distance (in km) from home to the town. Time going out T1 = D / 50 hours. Time coming back T2 = D / 45 hours. Given that the return journey takes 1 hour longer: D / 45 = D / 50 + 1. Multiply both sides by 450 to clear denominators. This gives 10D = 9D + 450. So 10D - 9D = 450 which implies D = 450 km.

Verification / Alternative check:
With D = 450 km, time from home to town is 450 / 50 = 9 hours. Time for the return trip is 450 / 45 = 10 hours. The difference between these times is 1 hour, exactly as stated in the problem. This confirms that the distance 450 km is correct.

Why Other Options Are Wrong:
If D were 350 km, times would be 7 hours and about 7.78 hours, which differ by less than an hour. If D were 700 km, times would be 14 hours and about 15.56 hours, a difference of 1.56 hours. For 900 km, the difference in times would be even larger. Only 450 km results in a difference of exactly 1 hour between onward and return journey times.

Common Pitfalls:
A common mistake is to think that distance is proportional to the difference in speeds alone, without using the time relation. Another error is to set up the equation backwards, for example writing D / 50 = D / 45 + 1, which reverses the problem’s condition. Carefully translating the statement "return journey takes one hour longer" into the equation is essential for success.

Final Answer:
Sravan covers a one way distance of 450 km between his home and the town.