Gilbert and Brian drove 604 miles in 11.6 hours. Gilbert drove the first part of the trip and averaged 45 miles per hour. Brian drove the remainder of the trip and averaged 65 miles per hour. For what length of the time did Gilbert drive?

The length of hours Gilbert drove is 7.5 hours.

The length of hours Brian drove is 4.1 hours.

Step-by-step explanation:

Let 'x' be the hours Gilbert drove.

Let 'y' be the hours Brian drove.

x+y = 11.6  (1)

45x+65y = 604 (2)

Multiply (1) by 45 and subtract (2) from (1)

 45x+45y = 522

-(45x+65y = 604)

       -20y = -82

y = 82/20

y = 4.1 hours

The length of hours Brian drove = 4.1 hours

Substitute y=4.1 in (1)

x+4.1 = 11.6

x = 7.5 hours

The length of hours Gilbert drove = 7.5 hours

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step-by-step explanation: ; )