let

c = the speed of the current, c>=0

v = the speed of the boat in still water, v>=0

d = 210 km the distance downstream and back

d/2 = 210/2 = 105 mi the distance traveled in each direction

t1 = 10 hr the time of the downstream trip

t2 = 70 hr the time of the upstream trip

the speed of the boat when moving upstream is: v - c

the speed of the boat when moving downstream is: v + c

since speed = distance/time => distance = time*speed

t1(v + c) = d/2

t2(v - c) = d/2

by solving the system of equations:

10(v + c) = 210/2

70(v - c) = 210/2

we find:

v = 6 mph

c = 4.5 mph

click here to see the step by step solution of the system of equations

the speed of the boat in still water is 6 mph.

the speed of the current is 4.5 mph.