Question

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.

Answer 1

Answer:

Time of driving of Maria = 1.8 hours

Step-by-step explanation:

Let a be time drove by Carlos and b be the time drove by Maria.

Carlos and Maria drove a total of 233 miles in 4.4 hours.

Total time = 4.4 hours

           a + b = 4.4 ------------------eqn 1

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.    

    Speed of Carlos =   55 miles per hour

    Speed of Maria =   50 miles per hour      

Total distance = 233 miles

That is

              55 a + 50 b = 233----------------------eqn 2

eqn 1 x 50

              50 a + 50 b = 220---------------------------eqn 3

eqn 3 - eqn 2

             55 a + 50 b -    50 a - 50 b   = 233 - 220

                  5a = 13

                   a = 2.6

Substituting in eqn 1

                2.6 + b = 4.4

                          b = 1.8

Time of driving of Maria = 1.8 hours

       

Answer 2

Let x - hours Carlos drove ; Let y - hours Maria drove

Equation 1: x + y = 4.4
x = 4.4 - y

Equation 2: 55x + 50y = 233
55(4.4 - y) + 50y = 233
242 - 55y + 50y = 233
-5y = 233-242
-5y = -9
y=9/5 or 1.8 hours Maria drove

To find time Carlos drove:
x=4.4 - 1.8
x = 2.6 hours