Distance of first part of trip = 55x
distance of 2nd part of trip = 70y
55x + 70y = 30
more information is needed to complete the question.
As it stands there would be an infinite number of solutions.
e.g. suppose he drove 12 minutes at 55 mph
distance = 1/5(55) miles = 11 miles
then 11 + 70y = 30
70y = 19
y = 19/70 hours = appr 16.3 minutes
btw, there would be restrictions: Suppose he drove the whole distance
at 55 mph, then x would be 0.545.. , and there would be no time
left to go at 70 mph.
so x < .545 , similarly y < 30/70 hours or y < 0.429 which happen to be the
x and y intercept values of the equation.