The dimensions of a field are (a unit×a unit). A cow grazed at the rate of b sq. Unit/minute. Find the time required to graze ¾ of the field.

To solve this problem, we'll break it down into steps.

1. **Calculate the total area of the field**:
   Since the dimensions of the field are \(a \times a\) units, the total area of the field is:
   \[
   \text{Total Area} = a \times a = a^2 \text{ square units}
   \]

2. **Determine the area to be grazed**:
   The cow needs to graze ¾ of the field. Therefore, the area to be grazed is:
   \[
   \text{Area to be grazed} = \frac{3}{4} \times a^2 = \frac{3a^2}{4} \text{ square units}
   \]

3. **Find the time required to graze this area**:
   The cow grazes at a rate of \(b\) square units per minute. Thus, the time required to graze \(\frac{3a^2}{4}\) square units is:
   \[
   \text{Time required} = \frac{\text{Area to be grazed}}{\text{Grazing rate}} = \frac{\frac{3a^2}{4}}{b} = \frac{3a^2}{4b} \text{ minutes}
   \]

So, the time required to graze ¾ of the field is \(\frac{3a^2}{4b}\) minutes.

Would you like more details or have any questions?

Here are some related questions:
1. How would the time change if the grazing rate doubled?
2. What if the cow grazed the entire field?
3. How would the formula change if the field were rectangular with dimensions \(a \times c\)?
4. How long would it take to graze half of the field?
5. What if the grazing rate decreased over time?

**Tip:** Always ensure units are consistent when solving area and rate problems.

Discover how to calculate the time needed for a cow to graze 3/4 of a field based on its dimensions and grazing rate. Learn the step-by-step solution involving area calculations and rates, suitable for Grades 7-9.

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