Math HW, please help: At its maximum speed, a motorboat can travel 10 miles downstream on a river in 20 minutes. It takes 30 minutes for the boat to travel back upstream the same 10 miles, also at maximum speed.
Write a system of two equations that could be used to find the maximum speed of the motorboat in still water. Let b represent the maximum speed of the motorboat in miles per hour and let r represent the speed of the river's current in miles per hour. Convert the times into hours. Solve the system of equations for b and r to determine the boat's maximum speed in still water and the speed of the river's current.

use this formula:

p(a\b) = p(a and b)/p(b).

take it from here.

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