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?

Answer 1

The speed of Nancy driving in the storm is $\boxed{36{\text{ mph}}}.$

Further explanation:

The formula for speed is given as,

$\boxed{s = \dfrac{d}{t}}$

Here, $s$ represents the speed, $d$ represents the distance, and $t$ represents time.

Given:

Nancy drove 50 miles in the good weather and she doves 68 miles in the storm.

She took 3 hour drive.

Calculation:

Consider the speed of Nancy in good weather be $x+9{\text{ mph}}.$

The speed of Nancy in storm will be $\left({x }\right){\text{ mph}}.$

The formula for time can be expressed as,

$\boxed{{\text{Time}}=\frac{{{\text{distance}}}}{{{\text{speed}}}}}$

The time taken to drive 50 miles in good weather can be calculated as follows,

${t_1} = \dfrac{x+9}{{50}}$

The time taken to drive 68 miles in storm can be calculated as follows,

${t_2} = \dfrac{{x}}{{68}}$

The total time t is the sum of ${t_1}$ and ${t_2}.$

$\begin{aligned}3&=\frac{{50}}{{x + 9}}+\frac{{68}}{x}\\3&= \frac{{50x + 68x + 612}}{{x\left( {x + 9}\right)}}\\3&=\frac{{50x + 68x + 612}}{{{x^2} + 9x}}\\3\times \left( {{x^2} + 9x} \right)&= 118x + 612\\3{x^2} + 27x&= 118x + 612\\3{x^2} - 91x - 612&=0\\\end{aligned}$

Further solve the above equation.

$\begin{aligned}3{x^2} + 17x - 108x - 612&= 0\\x\left( {3x + 17} \right) - 36\left( {3x + 17}\right)&= 0\\\left( {x - 36} \right)\left( {3x + 17} \right)&= 0\\\end{aligned}$

The speed in the storm can be obtained as follows,

$\begin{aligned}x - 36&=0\\x&=36\\\end{aligned}$

Neglect the second value of x as the speed cannot be negative.

The speed of Nancy driving in the storm is $\boxed{36{\text{ mph}}}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: Felicia, home, Ferrari, Rome, Sorrento, average, returning, Capri, boat, average speed, far, distance, speed, time, returning, averaged, 60 mph.

Answer 2

Answer:    

Speed in the storm is 36 miles per hour.

Step-by-step explanation:

Given : 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.

To find : What was her speed driving in the storm?

Solution :

The relation between speed, distance and time is

$\text{Distance}=\text{Speed}\times\text{Time}$

Let s be the speed in the storm, miles per hour

When there is no storm.

Speed = s+9 miles per hour

Distance = 50 miles

Time is $T=\frac{D}{S}=\frac{50}{s+9}$

When there is storm

Speed = r

Distance = 68 miles

Time is $T=\frac{68}{s}$

Total time taken = 3 hour

Therefore, In the journey total time is

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

Solving the equation,

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

$\frac{50s+68s+612}{s^2+9s}=3$

$118s+612=3s^2+27s$

$3s^2-91s-612=0$

Solving the quadratic equation by middle term split,

$3s^2+17s-108s-612=0$

$s(3s+17)-36(3s+17)=0$

$(s-36)(3s+17)=0$

$(s-36)=0,(3s+17)=0$

Either s=36 or s=-17/3

Speed is not negative

Therefore, s=36 mph

Speed in the storm is 36 miles per hour.