Exercise 26 Page 256

a To calculate the time it takes to travel a given distance, we can use the following formula.

d d r t = r \cdot t = Distance = Rate = Time

If she travels

1

block per minute this is her speed, or rate,

r .

The total distance she has to travel is

24

blocks. Since both the rate and the distance are expressed in blocks, we can calculate the time it takes for her to travel the distance.

d = r \cdot t

SubstituteII

$d = 24$ , $r = 1$

24 = 1 \cdot t

OneMult

$1 \cdot a = a$

24 = t

RearrangeEqn

Rearrange equation

t = 24

1

block per minute, it takes Meredith

24

minutes to travel

24

blocks. To find the time it takes her to travel the same distance with a speed of

2

blocks per minute, we substitute

r = 2

into the formula.

d = r \cdot t

SubstituteII

$d = 24$ , $r = 2$

24 = 2 \cdot t

DivEqn

$LHS / 2 = RHS / 2$

12 = t

RearrangeEqn

Rearrange equation

t = 12

2

blocks per minute, it takes Meredith

12

minutes to travel

24

blocks.

b Using the formula from Part A, we can set

d

equal to

24

and calculate the time for the different speeds.

r 3468101224 24 = r t 24 = 3 t 24 = 4 t 24 = 6 t 24 = 8 t 24 = 10 t 24 = 3 t 24 = 3 t t 8643 2.4 21

Now we can copy and complete the table.

Speed Time 12421238466483 10 2.4 122241

c When Meredith travels faster, it takes her less time to reach her friend's house. When she doubles her speed, it takes half the time. If she triples her speed, it takes a third of the time, and so on.

d In proportional relationships if one quantity increases, the other must too. Since the faster Meredith travels the less time it takes her to reach her friend's house, the relationship cannot be proportional.

Subchapter links

5.1.1 Representing Exponential Growth p.250-252

5.1.2 Rebound Ratios p.255-256

5.1.3 The Bouncing Ball and Exponential Decay p.259-260