Half an hour after leaving her house Beverly was 20 miles fr

Half an hour after leaving her house Beverly was 20 miles from home. At this point she merged onto the highway and was traveling at a constant speed for the next several hours. Four hours after leaving her house Beverly was 200 miles from home. How far did Beverly travel in 1 hour while traveling at a constant speed? How far did Beverly travel in 0.25 hours while traveling at a constant speed? How far did Beverly travel in 1.85 hours while traveling at a constant speed? How long did it take Beverly to travel 35 miles while traveling at a constant speed? How long did it take Beverly to travel 1 mile while traveling at a constant speed?

Solution

Case-1 :

Assuming constant speed from starting till 4hrs

At 0.5 hrs Beverely was 20 miles from home

After 4 hrs she was 200 miles

Lets form a linear equation from these two point.

Let d be distance and t be time.

( 0.5 , 20) and ( 4, 200)

slope = ( 200 -20)/( 4-0.5) = 180/3.5 =51.42 mil/hr

d = 51.42t +c .Use (0.5 , 20) to find c:

20 = 51.42*0.5 +c ---> c= -5.71

d = 51.42t -5.71

So, a) How far did Beverly travel in 1 hour while traveling at a constant speed?

t = 1hr d = 51.42 - 5.71 = 45.71 miles

b) How far did Beverly travel in 0.25 hours while traveling at a constant speed?

t = 0.25 hr ; d = 51.42*0.25 - 5.71 = 7.15 miles

c) How far did Beverly travel in 1.85 hours while traveling at a constant speed?

t = 1.85hr ; d= 51.42*1.85 - 5.71 = 89.53 miles

d) How long did it take Beverly to travel 35 miles while traveling at a constant speed?

d= 35 miles

35 = 51.42t - 5.71

t = 0.79 hr

e) How long did it take Beverly to travel 1 mile while traveling at a constant speed?

1 = 51.42t - 5.71

t = 0.13 hr

Case-2:

It may be piecewise function

part1: home (0, 0) and ( 0.5, 20)

part 2: after merging to highway ( 0.5, 20) and (4, 200)

So, part 1: d = 40t for 0<=t<=0.5 hrs

part 2 : d =   51.42t - 5.71 for 0.5 <t <= 4 hrs

So, a) How far did Beverly travel in 1 hour while traveling at a constant speed?

t = 1hr ;

d = 0.5 for 0.5hr

d= 51.42*0.5 - 5.71 = 20 miles

So total d = 40 miles in 1 hr

b) How far did Beverly travel in 0.25 hours while traveling at a constant speed?

t = 0.25 hr ; d =40*0.25 = 10 miles

c) How far did Beverly travel in 1.85 hours while traveling at a constant speed?

t = 1.85hr ;

d=20 miles for 0.5 hr

d = 51.42*1.35 - 5.71 = 63.707 miles

So, total d =83.71 miles

d) How long did it take Beverly to travel 35 miles while traveling at a constant speed?

t = 0.5hr for 20miles

Then , 15 = 51.42t - 5.71

t= 0.40 hr

So total time , t = 0.9 hrs

e) How long did it take Beverly to travel 1 mile while traveling at a constant speed?

1 mile ; d= 40t

1 = 40t

t = 0.025 hr