Deepesh walks a distance of 60 km at his usual speed. If he had walked 20 km/h faster, he would have saved 1 hour in travel time. What is his usual walking speed (in km/h)?

Introduction / Context:
This time and distance question focuses on how a change in speed affects total travel time over a fixed distance. Deepesh covers 60 km, and we are told how much time he would save if his speed increased by a fixed amount. The key is to set up a clear equation relating the two travel times and then solve for his usual speed.

Given Data / Assumptions:

- Distance travelled = 60 km.
- Usual speed of Deepesh = v km/h (unknown).
- Increased speed = v + 20 km/h.
- Time saved by walking faster = 1 hour.
- Motion is along a straight path with constant speeds in each scenario.

Concept / Approach:
Travel time is equal to distance divided by speed. The usual travel time is 60 / v hours, and the faster travel time is 60 / (v + 20) hours. The problem statement says that the time difference between these two is exactly 1 hour. This allows us to form an equation in a single variable v and solve it using algebraic methods for quadratic equations.

Step-by-Step Solution:
Usual time = 60 / v hours. Time at faster speed = 60 / (v + 20) hours. Given that the time saved is 1 hour: 60 / v - 60 / (v + 20) = 1. Multiply both sides by v (v + 20): 60 (v + 20) - 60 v = v (v + 20). Simplify left side: 60 v + 1200 - 60 v = 1200. So 1200 = v^2 + 20 v. Rearrange: v^2 + 20 v - 1200 = 0. Solve this quadratic equation. The positive root is approximately v = -10 + 10 * sqrt(13), which is about 26.06 km/h. This value is not equal to 100, 120, or 150 km/h.

Verification / Alternative check:
Using v approximately 26.06 km/h, usual time = 60 / 26.06 hours which is about 2.30 hours. Faster speed = v + 20 is about 46.06 km/h, so faster time = 60 / 46.06 which is about 1.30 hours. The difference between the two times is approximately 1 hour, matching the condition in the question. This confirms that our computed speed is correct even though it does not appear explicitly among the listed numeric options.

Why Other Options Are Wrong:
100, 120, and 150: If any of these were the usual speed, then adding 20 km/h would give an even larger speed and the time difference between the two speeds for a 60 km journey would be much smaller than 1 hour. Substituting them into the equation 60 / v - 60 / (v + 20) = 1 quickly shows they do not satisfy the condition.

Common Pitfalls:
Many students guess one of the large integer speeds or attempt to treat 20 km/h as a small correction without solving the quadratic carefully. Others forget that both speeds involve the same distance of 60 km. Always write the two time expressions clearly and form the exact equation rather than relying on rough estimation. Also remember that the correct choice in multiple choice questions can be “None of these” when the calculated value does not match any given number.

Final Answer:
Deepesh's usual walking speed is approximately 26.06 km/h, so among the given options the correct choice is None of these.