Mathematical model is this system of 2 equations for 2 unknowns

x + y = 210,

 +  = 6.

where x is the distance the driver covered at the speed of 60 mph, y is the distance covered at the reduced speed of 10 mph.

The system is consisted and x = 180 mi, y = 30 mi is one possible solution.
Hence, this solution is unique.

The problem is solved.

Let distance at reduced speed (10 mph) be D

Then distance traveled at 60 mph = 210 – D

Time traveled at 10 mph: 

Time traveled at 60 mph: 

We then get: 

6D + 210 – D = 360 --------- Multiplying by LCD, 60

6D – D = 360 – 210

5D = 150

D, or distance covered at reduced speed (10 mph) = , or  miles 

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