Question

Solve the following problems using linear functions.

a. Suppose there’s a linear relationship between your height and your shoe size: s = (1/10)h + 5, where h is measured in inches. If you’re 5 feet, 10 inches tall, what size shoes do you take? (Remember that 1 foot = 12 inches.)

b. Runner A and Runner B are competing in a race. Runner B is given a 10-meter head start and is therefore positioned 10 meters in front of the starting line. The starting gun sounds, and Runner B runs at a constant speed of 2.5 meters per second (m/s). After 10 seconds, how far is Runner B from the starting line?

Answer 1

Answer: a.) I take a shoe size 12

b.) Runner B is 35 m from starting line

Explanation:

a) The variable h (height) is in inches, so, first, transform feet in inches:

1 ft = 12 in

5ft = 5.12 = 60 in

My height is 5ft 10in, then, my height in inches is: h = 60 + 10 = 70

To determine my shoe size:

`s=(1)/(10)(70)+5`

s = 12

For me, who is 5ft 10in tall, my shoe size is 12.

b) Runner B is 10m in front of the starting line, which means runner's initial position is 10. Linear relationship between speed and position is given by:

`x=x_(0)+v.t`

where

x₀ is initial position

v is speed

t is time

Replacing and solving:

x = 10 + 2.5t

x = 10 + 2.5(10)

x = 35

After 10s, Runner B is 35 meters ahead of the starting line