Respuesta :
If the amount of time it takes to climb the hill is x hours, then 3x is the distance of the hill. In addition, if the amount of time it takes to go back down is y, then 5y is the distance of the hill too, so 5y=3x. Since it takes 40 minutes longer (2/3rds of an hour) to climb up the hill, y+2/3=x, making it 5y=3(y+2/3)=3y+6/3=2+3y using the distributive property. Subtracting 3y from both sides, we get 2y=2. Dividing both sides by 2, we get y=1. Multiplying that by 5, we get that 5*1=the hike (1 way)=5 miles.
The length of the hike is [tex]\boxed{\bf 5\text{ miles}}[/tex].
Further explantaion:
Given:
The speed of the Ted to up hill the hike is [tex]3\text{ mph}[/tex].
The speed of the Ted to going back down is [tex]5\text{ mph}[/tex].
The diffrence of time between climbing and going back down is [tex]40\text{min}[/tex].
To find: The length of the hike.
Calculation:
Consider the time taken to reach at the top of the hil is [tex]t_{1}[/tex], the time taken to reach the bottom of the hill is [tex]t_{2}[/tex] and the length of the hike is [tex]x[/tex].
The time taken to reach the top of the hill is,
[tex]\boxed{t_{1}=\dfrac{x}{3}\text{ hour}}[/tex]
The time taken to reach the bottom is
[tex]\boxed{t_{2} =\dfrac{x}{5}\text{ hour}}[/tex]
Convert [tex]40[/tex] minutes into hour as,
[tex]\begin{aligned}40\text{ min}&=\dfrac{40}{60}\\&=\dfrac{2}{3}\text{ hour}\end{aligned}[/tex]
The diffrence of time between climbing and going back down is [tex]40[/tex] minutes.
Express the above expresssion in equation form,
[tex]\begin{aligned}\dfrac{x}{3}-\dfrac{x}{5}&=\dfrac{2}{3}\\ \dfrac{5x-3x}{15}&=\dfrac{2}{3}\\ \dfrac{2x}{15}&=\dfrac{2}{3}\\ \dfrac{x}{5}&=1\\ x&=5\end{aligned}[/tex]
Therefore, the length of the hike is [tex]\boxed{\bf 5\text{ miles}}[/tex].
Learn more:
1. Speed https://brainly.com/question/4278023
2. Units and period https://brainly.com/question/558692
Answer details:
Grade: High school.
Subject: Mathematics
Chapter: Time and distance.
Keywords: Equations, units, measurement , meter, second, meter per second, meter per second square, position, object, time, velocity, Ted, hill, hike, 5 miles.
