Carlos and Maria drove a total of 233 miles in 4.4 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.

Question

anonymous · Answer

Subscripts: c = carlos  and  м = maria 

     Dc + Dм = 233 mi ... distances 
     Dc = 233  –  Dм ... equation 1 

       Tc + Tм = 4.4 hrs ... times 
          Tc = 4.4  –  Tм ... equation 2 

 Distance = Velocity • Time 

    Dм = (Vм) • (Tм) ... Maria's equation 
    Dм = (50) • (Tм) ... equation 3 


            Tc = (Dc) ⁄ (Vc) ... equation 4 ... Carlos's equation 

            Tc = (Dc) ⁄ 55 ... substitute eqs. 1 & 2 

           4.4 – Tм = (233  –  Dм) ⁄ 55 

         55(4.4 – Tм) = 233  –  Dм ... substitute eq. 3 

         55(4.4 – Tм) = 233  –  50(Tм) 

        242  –  55Tм = 233  –  50(Tм) 

             5Tм = 9 

              Tм = 9 ⁄ 5 = 1.8 hours  ...  Maria's time