Respuesta :
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
[tex]\text{Distance}=\text{Speed}\times\text{Time}[/tex]
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 [tex]T=\frac{D}{S}=\frac{50}{s+9}[/tex]
When there is storm
Speed = r
Distance = 68 miles
Time is [tex]T=\frac{68}{s}[/tex]
Total time taken = 3 hour
Therefore, In the journey total time is
[tex]\frac{50}{s+9}+\frac{68}{s}=3[/tex]
Solving the equation,
[tex]\frac{50s+68(s+9)}{s(s+9)}=3[/tex]
[tex]\frac{50s+68s+612}{s^2+9s}=3[/tex]
[tex]118s+612=3s^2+27s[/tex]
[tex]3s^2-91s-612=0[/tex]
Solving the quadratic equation by middle term split,
[tex]3s^2+17s-108s-612=0[/tex]
[tex]s(3s+17)-36(3s+17)=0[/tex]
[tex](s-36)(3s+17)=0[/tex]
[tex](s-36)=0,(3s+17)=0[/tex]
Either s=36 or s=-17/3
Speed is not negative
Therefore, s=36 mph
Speed in the storm is 36 miles per hour.
The speed of Nancy driving in the storm is [tex]\boxed{36{\text{ mph}}}.[/tex]
Further explanation:
The formula for speed is given as,
[tex]\boxed{s = \dfrac{d}{t}}[/tex]
Here, [tex]s[/tex] represents the speed, [tex]d[/tex] represents the distance, and [tex]t[/tex] 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 [tex]x+9{\text{ mph}}.[/tex]
The speed of Nancy in storm will be [tex]\left({x }\right){\text{ mph}}.[/tex]
The formula for time can be expressed as,
[tex]\boxed{{\text{Time}}=\frac{{{\text{distance}}}}{{{\text{speed}}}}}[/tex]
The time taken to drive 50 miles in good weather can be calculated as follows,
[tex]{t_1} = \dfrac{x+9}{{50}}[/tex]
The time taken to drive 68 miles in storm can be calculated as follows,
[tex]{t_2} = \dfrac{{x}}{{68}}[/tex]
The total time t is the sum of [tex]{t_1}[/tex] and [tex]{t_2}.[/tex]
[tex]\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}[/tex]
Further solve the above equation.
[tex]\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}[/tex]
The speed in the storm can be obtained as follows,
[tex]\begin{aligned}x - 36&=0\\x&=36\\\end{aligned}[/tex]
Neglect the second value of x as the speed cannot be negative.
The speed of Nancy driving in the storm is [tex]\boxed{36{\text{ mph}}}.[/tex]
Learn more:
1. Learn more about unit conversion https://brainly.com/question/4837736
2. Learn more about non-collinear https://brainly.com/question/4165000
3. Learn more aboutbinomial and trinomialhttps://brainly.com/question/1394854
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.
