Answer:
Wayne walked 3 miles, both Winston and Wilfred walked 2.5 miles
Step-by-step explanation:
Create equations out of the given information...
Equation 1: "Winston and Wilfred walked the same number of miles", becomes
Winston = Wilfred (the walked and equal amount of miles)
Equation 2: "Winston walked 2 miles less than 3/2 the miles Wayne walked" becomes
Winston = (3/2)Wayne - 2 (2 less than 3/2 of Wayne's effort)
Equation 3: "Wilfred walked 3/2 miles more than 1/3 the miles Wayne walked" becomes
Wilfred = (1/3)Wayne + 3/2 (3/2 more than 1/3 of Wayne's effort)
Since Winston and Wilfred walked the same number of miles, equations 2 and 3 are equal. Set them equal to each other and solve for how many miles Wayne walked...Treat 'Wayne' as a variable
(3/2)Wayne - 2 = (1/3)Wayne + 3/2
(3/2)Wayne - (1/3)Wayne = 2 + 3/2 (get variables on one side of the
equation, and constants on the
other side)
(7/6)Wayne = 7/2 (combine fractions on both sides of the
equation)
(6/7)(7/6)Wayne = (7/2)(6/7) (multiply both sides by the reciprocal
of 7/6 to get rid of the fraction on the
left side)
Wayne = 42/14 (Simplify the right side)
Wayne = 3 (reduce the fraction)
So Wayne walked 3 miles. Now plug '3' in for 'Wayne' in equations 2 and 3 to solve the rest...
Equation 2: Winston = (3/2)(3) - 2 (Wayne becomes '3')
Winston = 9/2 - 2
Winston = 9/2 - 4/2
Winston = 5/2 or 2.5 miles
Since Winston = Wilfred (equation 1) we know that Wilfred = 2.5 miles
