Q. 45 - Precalculus Enhanced with Graphing Utilities

Question

The following sketch represents the distance d (in miles) that Kevin was from home as a function of time t (in hours). Answer the questions based on the graph. In parts (a) – (g), how many hours elapsed and how far was Kevin from home during this time? 

$$\begin{gathered} \left(a\right) \mathrm{From} t=0 \mathrm{to} t=2 \\ \left(b\right) \mathrm{From} t=2 \mathrm{to} t=2.5 \\ \left(c\right) \mathrm{From} t=2.5 \mathrm{to} t=2.8 \\ \left(d\right) \mathrm{From} t=2.8 \mathrm{to} t=3 \\ \left(e\right) \mathrm{From} t=3 \mathrm{to} t=3.9 \\ \left(f\right) \mathrm{From} t=3.9 \mathrm{to} t=4.2 \\ \left(g\right) \mathrm{From} t=4.2 \mathrm{to} t=5.3 \end{gathered}$$

(h) What is the farthest distance that Kevin was from home? 

(i) How many times did Kevin return home? 

Step-by-Step Solution

Answer

(a) 2 hours, 0 to 3 miles

(b) 0.5 hours, 3 miles

(c) 0.3 hours, 0 to 3 miles

(d) 0.2 hours,  0 miles

(e) 0.9 hours, 0 to 2.8 miles

(f) 0.3 hours, 2.8 miles

(g) 1.1 hours, 0 to 2.8 miles

(h) 3 miles

(i) 2

Step 1. Given information

We have been given a sketch that represents the distance d (in miles) that Kevin was from home as a function of time t (in hours). 

We have to find how many hours elapsed and how far was Kevin from home during the given time interval.

Part (a) Step 2. Find hours elapsed and distance of Kevin from home during this time

Time elapsed during this interval $=2-0=2 hours$

Kevin is at a distance of 0 to 3 miles from home during this interval.

Part (b) Step 1. Find hours elapsed and distance of Kevin from home during this time

Time elapsed during this interval$=2.5-2=0.5 hours$

Kevin is at a distance 3 miles from home during this interval.

Part (c) Step 1. Find hours elapsed and distance of Kevin from home during this time

Time elapsed during this interval$=2.8-2.5=0.3 hours$

Kevin is at a distance of 0 to 3 miles from home during this interval.

Part (d) Step 1. Find hours elapsed and distance of Kevin from home during this time

Time elapsed during this interval$=3-2.8=0.2 hours$

Kevin is at a distance of 0 miles from home during this interval.

Part (e) Step 1. Find hours elapsed and distance of Kevin from home during this time

Time elapsed during this interval $=3.9-3=0.9 hours$.

Kevin is at a distance of 0 to 2.8 miles from home during this interval.

Part (f) Step 1. Find hours elapsed and distance of Kevin from home during this time

Time elapsed during this interval$=4.2-3.9=0.3 hours$

Kevin is at a distance of 2.8 miles from home during this interval.

Part (g) Step 1. Find hours elapsed and distance of Kevin from home during this time

Time elapsed during this interval$=5.3-4.2=1.1 hours$

Kevin is at a distance of 0 to 2.8 miles from home during this interval.

Part (h) Step 1. Find the greatest d coordinate on the graph

The greatest d coordinate on the graph is 3. 

Therefore, the farthest distance that Kevin from home was 3 miles.

Part (i) Step 1. Find how many times the distance of the Kewin is zero from nonzero

From the graph, we can see that 2 times the distance of the Kewin is zero from nonzero.

Therefore, 3 times Kevin returned home.