Question

Henry sends his hawk with a message to his uncle. The hawk flies out against the wind and returns with the wind, spending 3 hours on the whole trip. How far is Henry's uncle from Henry if the speed of the wind is 5 mph, and the hawk flies 50 mph in quiet weather?

Answer 1

Answer:

Distance between Henry and his uncle is 74.25km.

Step-by-step explanation:

Speed of Hawk with wind = 50+5

                                           =55km/hr

Speed of Hawk against wind = 50-5

                                               =45km/hr

we know that ,

        $Distance = speed \times time$

Let the distance between Henry and uncle is d,

According to the question ,

$\frac{d}{55} + \frac{d}{45} = 3$

$\frac{9d + 11d}{495} =3$

$20d = 3\times 495$

$d =\frac{3\times495}{20}$

d= 74.25km

Hence , the answer is 74.25km

Answer 2

The relation between speed, time, and distance is used. Then the distance between Henry's uncle from Henry is 74.25 miles.

What is speed?

The distance covered in an hour is called speed. it is a scalar quantity.

What is relative speed?

The concept of relative speed is used when two or more bodies moving with some speed are considered.

Henry sends his hawk with a message to his uncle.

The hawk flies out against the wind and returns with the wind, spending 3 hours on the whole trip.

We know the relation

$\rm speed = \dfrac{distance }{time}$

Let the distance between Henry's uncle from Henry be x.

The time of the trip is during the traveling remains constant. That is

$\rm T = T_1 + T_2\\\\T = \dfrac{x}{v_1} + \dfrac{x}{v_2}$

The speed of the wind is 5 mph, and the hawk flies 50 mph in quiet weather. Then we have

$\rm v_1 = 50 - 5 = 45\\\\v_2 = 50 + 5 = 55$

Then

$\begin{aligned} \rm \dfrac{x}{45} + \dfrac{x}{55} &= 3\\\\\rm \dfrac{9x + 11x }{495} &= 3\\\\\rm 9x + 11x &= 1485\\\\\rm 20x &= 1485\\\\\rm x &= 74.25 \end{aligned}$

Thus, the distance between Henry's uncle from Henry is 74.25 miles.

More about the speed link is given below.

https://brainly.com/question/862972