Question

Timothy walks from home to a mailbox. After

walking 15 min, he puts a letter in the mailbox.
Then he walks home at the same speed. The
graph shows his distance from the mailbox
as a function of time. What is his walking speed?
A 280 ft/min © 260 ft/min
B 270 ft/min
D 250 ft/min

Answer 1

The correct statements regarding the function are given as follows:

B. The x-intercept is (15, 0).

C. The y-intercept is (0, 3,750).

The intercepts of a function are two, the x-intercept and the y-intercept, defined as follows:

The set of x-intercepts is composed by the values of x for which the function crosses or touches the x-axis, that is, the values of x for which y = 0.

The y-intercept is the value of y for which x = 0, that is, the value of y when the function touches or crosses the y-axis.

A function can have only one y-intercept as a function must have only one output relative to the input x = 0, however it can have an infinity amount of x-intercepts.

From the definitions in these bullet points, the intercepts for this function are given as follows:

x-intercept: (15,0).

y-intercept: (0, 3750).

This means that statements B and C are correct.

Question

Timothy walks from home to a mailbox. After walking 15 min, he puts a letter in the mailbox. Then he walks home at the same speed. The graph shows his distance from the mailbox as a function of time. Select all the statements that are true of the function.

A. The x-intercept is (0, 3,750).

B. The x-intercept is (15, 0).

C. The y-intercept is (0, 3,750).

D. The y-intercept is (15, 0).

E. The y-intercepts are (0, 3,750) and (30, 3,750).

Answer 2

D. 250 feet per minute

Explanation:

According to this question, Timothy walks at constant speed. From Physics we know that speed is the magnitude of velocity and is determined by the following definition:

`v = (\Delta x)/(\Delta t)` (1)

Where:

`\Delta x` - Distance between home and mailbox, measured in feet.

`\Delta t` - Travel time, measured in minutes.

`v` - Walking speed of Timothy, measured in meters per second.

The distance is represented by the vertical axis of the graph, whereas the travelling time is from the horizontal axis.

If we know that
`\Delta x = 3,750\,ft` and
`\Delta t = 15\,min`, then the walking speed of Timothy is:

`v = (3,750\,ft)/(15\,min )`

`v = 250\,(ft)/(min)`

The walking speed of Timothy is 250 feet per minute. Hence, the right answer is D.