New to this math

Question

A motorboat travels 273 miles in 7 hours going upstream. It travels 413 miles going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

49 mph and 10 mph

time traveled = distance divided by rate of speed

b = boat speed, c = current speed

b-c = upstream speed

b+c = downstream speed

7 = 273/(b-c)

7 =413/(b+c)

7b+7c = 413

7b-7c = 273

14b = 413+273 = 686

b=68/614 = 49 mph = boat speed

7c = 413 -7(49) = 413 - 343 = 70

c = 70/7 = 10 mph = current speed