Question

Wayne, Winston, and Wilfred walked for an hour. Winston and Wilfred walked the same number of miles. Winston walked 2 miles less than 3/2 the miles Wayne walked. Wilfred walked 3/2 miles more than 1/3
the miles Wayne walked.​

Answer 1

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