Question 7

Explanation

We will calculate the work rate of each tractor (the portion of the field that can be plowed in one day) and sum the rates of tractor 1 and 3.

Calculating Tractor Work Rates

Tractor 1:

Time required = 3 days. Work rate per day = $\frac{1}{3}$ part.

Tractor 2:

Time required = $4 \frac{1}{5} = \frac{21}{5}$ days. Work rate per day = $\frac{1}{\frac{21}{5}} = \frac{5}{21}$ part.

Tractor 3:

Time required = $3.5 = \frac{7}{2}$ days. Work rate per day = $\frac{1}{\frac{7}{2}} = \frac{2}{7}$ part.

Calculating Combined Tractor 1 and 3

On the first day, only tractors 1 and 3 are used. Thus, the portion of the field that can be plowed is the sum of the work rates of these two tractors.

We find a common denominator of 21:

So, the portion of the field that can be plowed by both tractors is $\frac{13}{21}$ part.