A plane traveled 580 miles to its destination and then returned home. The trip there was into the wind. The trip back took 10 hours. Find the speed of the plane in still air and the speed of the wind

This is the complete question;

A plane traveled 580 miles to its destination and then returned home. The trip there was with the wind. It took 5 hours. The trip back was into the wind. The trip took 10 hours. Find the speed of the plane in still air and the speed of the wind

Speed of plane in still air = 116 miles/hr

Speed of wind = 87 miles/hr

Step-by-step explanation:

Let the speed of the plane in still air be p

Let the speed of the wind be w

Now, we know that speed = distance/time.

Thus, on the trip going, the time was spent was 5 hours while the distance is 580 miles.

Thus, the total speed on this trip going is; 580/5 = 116 miles/hr

Now, the question says this trip was with the wind. Thus it means the plane speed and wind speed aided the movement.

So, p + w = 116 miles/hr - - - - - (eq1)

Now, on the return trip of 10 hours , it says plane was into the wind which means plane speed minus wind speed.

Thus,

p - w = 580/10

p - w = 58 miles/hr - - - - - (eq2)

Add eq 1 to eq 2 to get ;

2p = 116 + 58

2p = 174

p = 87 miles/hr

Plug in this into eq 2 to get

87 - w = 58

w = 87 - 58 = 29 miles/hr

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

here is the

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