Question 286064
Use the formula:
{{{d = r*t}}} where: d = distance, r = rate(speed), and t = time of travel.
In this problem, the distance, d, is the same for the downstream trip and the upstream trip, so...
For the downstream trip, the speed of the boat relative to the shore equals the boat speed on the water plus the speed of the current, so we'll let r = the boat speed and S = the speed of the current.
{{{d[d] = (r+S)*t}}} Substitute r = 40 mph and t = 4 hrs.
{{{d[d] = (40+S)*4}}} Simplify.
{{{d[d] = 160+4S}}}
For the upstream trip, let r = the boat speed and S = the speed of the current.
{{{d[u] = (r-S)*t}}}
{{{d[u] = (40-S)*10}}} Simplify.
{{{d[u] = 400-10S}}} But the distances are equal, so...
{{{d[d] = d[u]}}}  then...
{{{160+4S = 400-10S}}} Add 10S to both sides.
{{{160+14S = 400}}} Subtract 160 from both sides.
{{{14S = 240}}} Divide both sides by 14.
{{{S = 17.146}}}
The speed of the current is 17.146 mph.