Question

During a walk a thon,noahs time in hours was,t,and distance in miles,d,are related by the equation 1/3d=t .A gragh of the equarion includes points (12,4)

Answer 1

Question:

During a walk-a-thon, Noah's time in hours was t, and distance in miles, d, are related by the equation $\frac{1}{3}d = t$.  A graph of the equation includes points (12,4).

1. Identify the independent variable.

2. What does the point (12,4) represent in this situation?

3. What point would represent the time it took to walk $7\frac{1}{2}$ miles?  

Answer:

(a) d

(b) He spent 4 hours to walk 12 miles

(c) $(7\frac{1}{2},2\frac{1}{2})$

Step-by-step explanation:

Given

$t = \frac{1}{3}d$

Solving (a): The independent variable

The independent variable, in this problem is the distance walked. Because the distance walked stands alone, and it is when the distance is known, that the time spent is known.

Hence:

The independent variable is distance (d)

Solving (b): What (12, 4) represents

This implies that:

$distance = 12$

$time\ spent = 4$

So: He spent 4 hours to walk 12 miles

Solving (c): Point to represent the time to walk $7\frac{1}{2}$ miles

This implies that:

$d = 7\frac{1}{2}$

Substitute $d = 7\frac{1}{2}$ in $t = \frac{1}{3}d$

$t = \frac{1}{3} * 7\frac{1}{2}$

Express as improper fraction

$t = \frac{1}{3} * \frac{15}{2}$

$t = \frac{5}{2}$

Express as mixed number

$t = 2\frac{1}{2}$

So: The point is, $(7\frac{1}{2},2\frac{1}{2})$