Chapter 1, Problem 27P

To determine

Total time taken by a person to mow a football field.

Answer to Problem 27P

Solution

The time taken by a person to mow a football field is 10h.

Explanation of Solution

Given:

The speed of mowers is 1km/h.

Width of the field is 0.5m.

Calculations:

Assume football field width 48.8 m

Width covered in 1 round = 0.5 m

Total number of rounds to mow a field:

  $\begin{array}{l}=\frac{48.8}{0.5}\\ \approx 98\end{array}$

Assume total length of football field = 91.55 m

Speed = 1km/h

Time taken to cover 1 pass = ?

  $\text{Speed = distance / time}$

  $\text{1 km/h = 91}\text{.55 m /time}$

  $\text{Time = 91}\text{.55}\left(\text{m}\right)\text{ / 1}\left(\text{km/h}\right)$

  $\text{ t = 91}\text{.55/1000}$

  $\text{ t = 0}\text{.09155 h}$

Total time taken is:

Assume 5 seconds are required to take on turn.

  $\begin{array}{l}\text{T=98×0}\text{.0915 }\left(\text{h}\right)\text{ + 97}\text{.5×5}\text{s}\\ \text{= 9}\text{.46 h}\\ \approx \text{10}\text{h}\end{array}$

Conclusion:The time taken by a person to mow a football field is 10h.