Question

1. A. What is James’s new texting speed if he practices for 1 month?


What is James's new texting speed if he practices for 2 months?

What is James’s new texting speed if he practices for 3 months?

Write an algebraic equation that gives James’s texting speed s for m months of practice.

2. A. Solve the equation from question 1d to determine how many months of practice it will take before James’s texting speed reaches 8 characters per second.

Answer 1

A. 2 + (1/2)* 1 = 2.5

B. 2 + (1/2)*2 = 3

C. 2 + (1/2)*3 = 3.5

D. s = 2 + (1/2)*m


2. 8 = 2 + (1/2)*m

6 = (1/2)m

m = 12

Answer 2

Answer:

1. a. 2.5 character per sec

b. 3 character per sec

c. 3.5 character per sec

d. $s=2 + \frac{1}{2}m$

2. 12 months

Explanation :

Here, the current speed of James = 2 character per second,

∵ His speed is increasing by $\frac{1}{2}$ character per second in each month,

1. a. So, his speed after one month = $2+\frac{1}{2}$ = 2 + 0.5 = 2.5 character per sec

b. After 2 months = $2+\frac{1}{2}\times 2$ = 2 + 1 = 3 character per sec

c. After 3 months = $2+\frac{1}{2}\times 3$ = 2 + 1.5 = 3.5 character per sec

d. Similarly, his speed after m months ( say s ),

$s=2 + \frac{1}{2}m$

Which is the required equation.

2. If s = 8 characters per second,

$8=2+\frac{1}{2}m$

$8-2=\frac{m}{2}$

$6=\frac{m}{2}$

$\implies m = 2\times 6=12$

Hence, after 12 months his texting speed will reach 8 characters per second.