Answer
He can row in still water at a speed of $8.7$ kilometers per hour and the speed of the current is $1.9$ kilometers per hour.
Work Step by Step
Terry Watkins rows $10.6$ kilometers in $1$ hour downstream and $6.8$ kilometers in $1$ hour upstream.
Let $r$ be how fast he can row in still water and let $c$ be the speed of the current. Both values are in kilometers per hour.
$r + c = 10.6$ Equation $(1)$ (Speed Downstream)
$r - c = 6.8$ Equation $(2)$ (Speed Upstream)
Equation $(1)$ + Equation $(2)$
$(r+c) + (r-c) = (10.6+6.8)$
$2r = 17.4$
$r=8.7$
Substitute $r$ into the Equation $(1)$.
$8.7 + c = 10.6$
$c = 1.9$
He can row in still water at a speed of $8.7$ kilometers per hour and the speed of the current is $1.9$ kilometers per hour.