A man is hired to plant trees for a continuous period of 10 hours. He can plant 10 trees in every hour of work, but after each hour of planting he takes a rest for 30 minutes before resuming. Assuming this pattern continues throughout the 10-hour period, how many trees does he plant in total?

Introduction / Context:

This time and work question involves periodic rest intervals. The man plants trees at a constant rate, but he does not work continuously, because he takes a break after every hour of planting. The challenge is to correctly interpret the 10-hour period and count how many full working hours fit into it, rather than simply multiplying rate by 10.

Given Data / Assumptions:

• Total engagement period for the job = 10 hours.
• During each full working hour, the man plants 10 trees.
• After every 1 hour of planting, he takes a rest of 30 minutes before starting the next working hour.
• The 10-hour period includes both working time and rest time.

Concept / Approach:

Each complete cycle consists of 1 hour of work followed by 0.5 hour of rest, for a total of 1.5 hours. During each cycle he plants 10 trees. We must find how many full working hours, and thus how many cycles, fit into 10 hours. In the final part of the period, if there is enough time for an additional working hour but not for another rest, he is still able to work that extra hour, as rest is taken after completing an hour of planting.

Step-by-Step Solution:

Verification / Alternative check:

We can create a rough timetable. He works from hour 0 to 1, rests from 1 to 1.5, works again from 1.5 to 2.5, rests from 2.5 to 3, and so on. After six such cycles he reaches time 9 hours. From 9 to 10 hours he can perform one more full working hour. This matches the cycle-based calculation and confirms that he completes 7 working hours in the 10-hour period.

Why Other Options Are Wrong:

Option 100 assumes he works all 10 hours without rest, ignoring the breaks.

Option 50 would correspond to only five working hours, which undercounts the available time.

Option 45 corresponds to 4.5 hours of work and does not align with the given schedule pattern of full working hours followed by breaks.

Common Pitfalls:

A very common mistake is to multiply 10 hours by 10 trees per hour and ignore rest, or to assume every 1.5 hours is a fixed cycle without considering that the last working hour does not need a break within the given time window. Carefully modeling the timeline helps avoid these errors.

Final Answer:

The man plants a total of 70 trees in 10 hours.