Question

This is a graph of the motion of a small boat traveling at a constant speed. Total Distance Traveled 12 10 8 Distance (Kilometers) 6 0 2 4 6 8 1012 Time (Hours) How far will the boat travel in 15 hours? O A. 25 km O B. 30 km O C. 15 km O D. 10 km

Answer 1

The speed of the boat is given by the gradient of the line.

Given two points (x1,y1) and (x2,y2) on a graph, the gradient of the line that passes through the two points is given by

`\text{ gradient = }(y_2-y_1)/(x_2-x_1)`

In this case,

the line passes through the points (0,0) and (2,2).

We can set (x1,x2) = (0,0) and (y1,y2) = (2,2)

Therefore,

`\begin{gathered} \text{ gradient = }(2-0)/(2-0)=(2)/(2)=1 \\ \text{therefore} \\ \text{the speed = 1km/h} \end{gathered}`

Given that a body travels with speed, s, and in time, t, the distance travelled, d, is given by

`d=st`

In this case,

s = 1km/h, and t = 15hours

Therefore,

Therefore, the boat travelled a distance of 15km