Arjay, Dorothy, Melissa, and Gray live in the same city. Arjay and Dorothy live 2 miles from each other. Dorothy and Melissa liv
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Since the Venus orbits round the sun, the sun is the center of the circular path of the revolution of the planet, Venus.
Thus, the distance of the planet, Venus fron the sun is given by the distance between the points (0, 0) and (41, 53).
Recall that the distance between two points
and 
is given by 
Thus, the distance between the points (0, 0) and (41, 53) is given by:
Given that each unit of the plane represents 1 million miles, therefore, the distance from the sun to the Venus is 67 million miles.
Thus, the distance of the planet, Venus fron the sun is given by the distance between the points (0, 0) and (41, 53).
Recall that the distance between two points
Thus, the distance between the points (0, 0) and (41, 53) is given by:
Given that each unit of the plane represents 1 million miles, therefore, the distance from the sun to the Venus is 67 million miles.
Distance traveled in clear weather = 50 miles
Distance traveled in thunderstorm = 15 miles
Let speed in clear weather = x
⇒ Speed in thunderstorm = x-20
Total time taken for trip = 1.5 hours
We need to determine average speed in clear weather (i.e. x) and average speed in the thunderstorm (i.e. x-20 ).
Total time taken for trip = Time taken in clear weather + Time taken in thunderstorm
⇒ Total time taken for trip = +
⇒ 1.5 = +
⇒ 1.5 =
⇒ 15*x*(x-20) = 10*[50*(x-20)+15*x]
⇒ 15x² - 300x = 500x - 10,000 + 150x
⇒ 15x² - 300x = 650x - 10,000
⇒ 15x² - 950x + 10,000 = 0
⇒ 3x² - 190x + 2,000 = 0
The above equation is in the format of ax² + bx + c = 0
To determine the roots of the equation, we will first determine 'D'
D = b² - 4ac
⇒ D = (-190)² - 4*3*2,000
⇒ D = 36,100 - 24,000
⇒ D = 12,100
Now using the D to determine the two roots of the equation
Roots are: x₁ = ; x₂ =
⇒ x₁ = and x₂ =
⇒ x₁ = and x₂ =
⇒ x₁ = and x₂ =
⇒ x₁ = 50 and x₂ = 13.33
So speed in clear weather can be 50 mph or 13.33 mph. However, we know that in thunderstorm was 20 mph less than speed in clear weather.
If speed in clear weather is 13.33 mph then speed in thunderstorm would be negative, which is not possible since speed can't be negative.
Hence, the speed in clear weather would be 50 mph, and in thunderstorm would be 20 mph less, i.e. 30 mph.