Two cars traveling toward each are 200 miles apart. Car A is traveling 20 miles per hour faster than car B. The cars pass after 2 hours. How fast is each car traveling?

Step-by-step explanation:

d = 200 miles

B rate = x

A Rate = x + 20

Each has traveled two hours

The total distance each travels after two hours is 200 miles (they pass each other).

d = r * t

2*x + 2*(x + 20) = 200      Remove the brackets

2x + 2x + 40 = 200           Combine like terms

4x + 40 = 200                   Subtract 40 from each side

4x = 200 - 40                  

4x = 160                           Divide by 4

x = 160/4

x = 40

There B's rate is 40 miles / hour

A's rate is 40 + 20 = 60 miles / hour

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form