Question

On the grid, sketch a graph to represent

Sandy's walk to school based on the
description below.
Sandy lives 200 m from school. One
morning she leaves for school at a
slow pace. On the way she meets a
friend and stops to talk för 10
minutes. Sandy realizes that she
forgot her homework and runs back
home to pick it up. It takes five
minutes to get home. Immediately she
heads back to school at a fast pace.

Answer 1

Please find attached, the required graph created on MS Excel

Explanation:

The distance between Sandy's house and the school = 200 m

The number of minutes Sandy talked to her friend for = 10 minutes

The time it took Sandy to return home to pick her homework = 5 minutes

Let x represent Sandy's location she stops to talk to her friend 10 minutes, we have;

The slope of the motion on the graph, m₁ = (x - 0)/(t - 0)

The slope of her motion running home to pick the up her homework, m₂ = (x - 0)/(5 - 0)

Given that t > 5, the slope on trip back home, m₁, is larger than are her initial slope, m₂

Therefore, where x = 125, we have;

The rate at which she returned home = m₂ = (125 m - 0)/(5 min - 0) = 25 m/min

Given that the same rate m₂ is what she used in heading back to school, we have;

The time it takes her to get to school = 200 m/(25 m/min) = 8 minutes

Therefore, whereby it took her 10 minutes to reach point x, we have the following coordinate points on the graph in a tabular form;

`\begin{array}{ccc} Time \ (minutes) \ x-axis&&Distance \ (meters) \ y-axis\\0&&0\\10&&25\\15&&0\\23&&200\end{array}`

The plot of the above point is completed using MS Excel as shown in the attached diagram.