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Chapter 2: Q. 45 (page 80)

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) 鈥� (g), how many hours elapsed and how far was Kevin from home during this time?

(a)Fromt=0tot=2(b)Fromt=2tot=2.5(c)Fromt=2.5tot=2.8(d)Fromt=2.8tot=3(e)Fromt=3tot=3.9(f)Fromt=3.9tot=4.2(g)Fromt=4.2tot=5.3

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

(i) How many times did Kevin return home?

Short Answer

Expert verified

(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 by step solution

01

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.

02

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

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

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

03

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

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

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

04

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=0.3hours

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

05

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

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

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

06

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

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

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

07

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=0.3hours

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

08

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=1.1hours

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

09

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.

10

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.

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