Question

An airplane’s average speed from San Diego to Dallas can be calculated using the function where t is the number of hours of travel. When there are tailwinds, the increased speed can be calculated using the function
w(s) = fs, where f is the percent increase as a decimal. On a given day, the tailwinds caused the average speed to increase by 2.5%, or w(s) = 1.025s.


Which function can be used to find the increased speed depending on the number of hours traveled?

Answer 1

Answer:

$w(s(t)) = \frac{1.392975}{t}$

Step-by-step explanation:

Given

$s(t) = \frac{1.359}{t}$ --- San Diego to Dallas

$w(s) = 1.025s$ ---- Increment in average speed

Required

A function that represents the increased speed from hours

This implies that, we calculate the composite function

$w(s(t))$

We have:

$w(s) = 1.025s$

This gives:

$w(s(t)) = 1.025s(t)$

Substitute: $s(t) = \frac{1.359}{t}$

$w(s(t)) = 1.025 * \frac{1.359}{t}$

Rewrite as:

$w(s(t)) = \frac{1.025 * 1.359}{t}$

$w(s(t)) = \frac{1.392975}{t}$