Question

nancy took a 3 hour drive. she went 50 miles before she got caught in a storm. then she drove 68 miles at 9 mph less than she had driven when the weather was good. what was her speed driving in the storm?

provide your answer below:

s = mph

Explanation:

Set up the rational equation

Let \(s\) be Nancy's speed driving in the storm (in mph).
Her speed in good weather is \(s + 9\) mph.
The total time is 3 hours:

$$ \frac{50}{s + 9} + \frac{68}{s} = 3 $$

Solve the quadratic equation

Multiply by \(s(s + 9)\):

$$
LATEXBLOCK0
$$

Using the quadratic formula:

$$
LATEXBLOCK1
$$

Since speed must be positive:

$$ s = \frac{91 + 125}{6} = \frac{216}{6} = 36 $$

Verify the solution

$$
LATEXBLOCK2
$$

Answer:

Nancy took a 3 hour drive. She went 50 miles before she got caught in a storm. Then she drove 68 miles at 9 mph less than she had driven when the weather was good. What was her speed driving in the storm?

Provide your answer below:

\(s =\) <blank>36</blank> mph