Your brother and sister took turns driving on a 580 mile trip that took 10 hours to complete. your brother drove at a constant speed of 55 miles per hour and your sister drove at a constant speed of 60 miles per hour. how long did each person drive.

Let the time the boy drove be x and that the girl drove be y:

x+y=10

thus

x=10-y ... i

distance=speed*time

the distance each one drove will be:

55x+60y=580 ... ii

substituting i in ii we get:

55 (10-y) + 60y=580

550-55y+60y=580

5y=30

y=6 hours

thus

x=10-6=4 hours

hence the boy drove for 4 hours and the girl for 4 hours