Acar travels 60 miles per hour, and a plane travels 15 miles per minute. how far does the car travel while the plane travels 600 miles?

The car travels 40 miles while the plane travels 600 miles.

Step-by-step explanation:

This problem can be solved by rules of three.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

In this problem, all the measures have direct relationship.

The first step is knowing how much the plane travels in a hour.

The problem states that in a minute, the plane travels 15 miles. How much does it travel in 60 minutes.

1 minute - 15 miles

60 minutes - x miles

x = 60*15

x = 900 miles

In a hour, the plane travels 900 miles.

Then we need to know how long it takes for the plane to travel 600 miles.

1 hour - 900 miles

x hours - 600 miles

900x = 600

x = 0.667 hours = 40 minutes.

Finally, we discover how much the car travels in 40 minutes.

The problem states that in a hour(60 minutes), the car travels 60 miles, so:

60 miles - 60 minutes

x miles - 40 minutes

60x = 2400

x = 40 miles.

The car travels 40 miles while the plane travels 600 miles.

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0