Brady rode his bike 70 miles in 4 hours. he rode at an average of 17 mph for t hours and at an average rate of speed of 22 mph for rest of the time. how long did brady ride at the slower speed? use the variable t to represent the time, in hours, brady rode at 17mph

Brady rode his bike for a total of 4 hours.  Let t1 represent the length of time over which he rode for at an average of 17 mph and let t2 repr. the time over which he road at an average 22 mph.

t1 + t2 must add up to 4 hours.  Obviously this means that t1 = 4 hrs - t2.

Distances (17 mph * t1 hrs) and (22 mph * t2 hrs) must add up to 70 miles.

Solve this system of linear equations for t1 and t2.  The answer required in this particular problem is t1, the length of time that Brady rode at an average 17 mph.

Alternatively, use t to represent the length of time during which he road at at an average 17 mph, and (4 hrs - t) to represent the time during which he road at an average 22 mph.