A man starts 20 minutes late but travels at 1.5 times his usual speed and reaches right on time. What is his usual travel time (in minutes) to reach the office?

Introduction / Context:
If you start late but increase speed, you can still arrive on schedule. Doubling logic: time is inversely proportional to speed. Here, increasing speed to 1.5× scales time by 2/3.

Given Data / Assumptions:

• Usual time = T hours.
• Faster time = (2/3)T hours (because speed is 1.5×).
• He starts 20 minutes = 1/3 hour late and still arrives on time.

Concept / Approach:
Because he arrives exactly on time, (2/3)T must equal T − 1/3. Solve for T, then convert to minutes if needed.

Step-by-Step Solution:

Verification / Alternative check:
At usual speed he would need 60 min; starting 20 min late would cause a 20 min delay, but at 1.5× speed his travel time is 40 min, exactly compensating.

Why Other Options Are Wrong:
30, 40, 50, 80 minutes fail (2/3)T = T − 20 min.

Common Pitfalls:
Using 1/1.5 = 3/2 incorrectly; mixing minutes/hours while solving.

Final Answer:
1 h