Mixed grazing rates for goats and sheep Either 4 goats or 6 sheep can graze a field in 50 days. If 2 goats and 9 sheep graze together, in how many days will they finish the field?

Introduction / Context:
This is a rates-combination problem using equivalent-team times. We find individual animal rates and sum them for the new team.

Given Data / Assumptions:

• 4 goats in 50 days ⇒ 1 job.
• 6 sheep in 50 days ⇒ 1 job.
• Team: 2 goats + 9 sheep.

Concept / Approach:
Compute per-day per-animal rates from the team times, add them, and invert to get time.

Step-by-Step Solution:

Verification / Alternative check:
If they worked 25 days, they would do 25 * (1/25) = 1 job, confirming correctness.

Why Other Options Are Wrong:
50, 75, 100 days correspond to incorrect combined rates.

Common Pitfalls:
Failing to convert team times into per-animal rates before recombining.

Final Answer:
25 days