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Question

Carlos and Maria drove a total of 197 miles in 3.8 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 47 miles per hour. for approximately how many hours did Maria drive

Answer 1

 Maria's rate was 47/hr

Carlos' rate was 55/hr

Maria's time was 3.8-t

Carlos' time was t

Maria's distance was 197-d

Carlos' distance was d

47(3.8-t)=197-d(Maria)

55t = d(Carlos)

 

47(3.8-t)=197-55t--->178.6-47t=197-55t---->-18.4 = -8t---->t≈1.5

3.8-1.5 = 2.3

 

Answer 2

Set up a d=rt table:

             

                d          r          t        

Carlos       d          55        t

Maria      197-d      47      3.8-t

 

Write the two equations:

 

Carlos      d=55t

Maria    197-d = 47(3.8-t)

 

Substitute 55t in for d in Maria's equation:

 

197-55t = 47(3.8 -t)    then distribute and simplify

197-55t = 178.6 - 47t

18.4 = 8t

2.3 = t

 

2.3 is Carlos' number of hours driving.  To find Maria's, subtract 2.3 from 3.8 total hours driven.

 

Maria drove 1.5 hours.

 

Answer 3

                           rate            time                        distance

Carlos                  55                x                             55x

Maria                   47               3.8 - x                       47(3.8-x)

 

Notice, if you know one of the peoples time, you can figure out the other person's time by subtracting it from 3.8

 

So 55x + 47(3.8 - x) = 197      the total distance, or the sum of the distances is 197.

 

Solve this and you get x, or carlos drove 2.3 hours, so Maria drove 3-8-2.3 = 1.5hrs.

 

Hope this helped.