Respuesta :
Answer: 25 miles
Step-by-step explanation:
Since, the total distance = 31 miles.
Let he walks x miles at the rate of 4 miles per hour.
⇒ he walks remaining (31-x) miles at the rate of 50 miles per hour.
According to the question,
[tex]\frac{x}{4} + \frac{31-x}{50} = 2[/tex]
⇒ [tex]\frac{25x}{100} + \frac{62-2x}{100} = 2[/tex]
⇒ [tex]\frac{25x+62-2x}{100}= 2[/tex]
⇒ [tex]\frac{23x+62}{100}= 2[/tex]
⇒ [tex]23 x + 62 = 200[/tex]
⇒ [tex]23 x = 200 - 62[/tex] ( by subtracting 62 on both sides )
⇒ [tex]23 x = 138[/tex]
⇒ [tex]x=\frac{138}{23}[/tex] ( Dividing both sides by 23 )
⇒ [tex]x = 6[/tex]
Thus, the distance he pays to the cab driver = 31-x= 31 - 6 = 25 miles.
Therefore, He pays to the cab driver for 25 miles.
Distance that must be paid to the taxi = 25 miles
Further explanation
Linear motion consists of 2: constant velocity motion with constant velocity and uniformly accelerated motion with constant acceleration
• At constant velocity motion:
the speed of vo = v = constant
acceleration = a = 0
Δx = vt or x = xo + vt
An equation of constant velocity motion
[tex]\large {\boxed {\bold {x = v \times \: t}}}[/tex]
x = distance = m
v = speed = m / s
t = time = seconds
so
[tex]\rm t=\dfrac{x}{v}[/tex]
A mountain path is 31 miles long
The distance traveled by tourists = x1
The distance traveled taxi = x2, such that
x1 + x2 = 31
x1 = 31-x2
total travel time (t) = 2 hours
tourist speed = v1 = 4 mph
taxi speed = v2 = 50 mph
time taken by tourists = t1
[tex]\rm \dfrac{x1}{v1}=\dfrac{x1}{4}[/tex]
the time taken by taxi = t2
[tex]\rm \dfrac{x2}{v2}=\dfrac{x2}{50}[/tex]
total time = t1 + t2
[tex]\rm 2=\dfrac{x1}{4}+\dfrac{x2}{50}\\\\2=\dfrac{25x1+2x2}{100}\\\\200=25(31-x2)+2x2\\\\200=775-25x2+2x2\\\\575=23x2\\\\x2=\boxed{\bold{25~miles}}[/tex]
Learn more
The distance of the elevator
brainly.com/question/8729508
resultant velocity
brainly.com/question/4945130
the average velocity
brainly.com/question/5248528
