Question

1. the time t (in days) that it takes to harvest a field varies inversely with the number n of farm workers. a farmer can harvest his crop in 20 days with 7 farm workers. how long will it take to harvest the crop if he hires 10 farm workers?

Explanation:

Step1: Define inverse variation formula

Inverse variation: \( t=\frac{k}{n} \), where \( k \) is constant.

Step2: Find constant \( k \)

Given \( t = 20 \), \( n = 7 \). Substitute: \( 20=\frac{k}{7}\), so \( k = 20\times7 = 140 \).

Step3: Calculate \( t \) for \( n = 10 \)

Use \( t=\frac{k}{n} \), \( k = 140 \), \( n = 10 \). Then \( t=\frac{140}{10}=14 \).

Answer:

14 days