let

v = the rate of the ship in still water

c = 1.9 mph the rate of the current

t1 = 9 hr the time of the travel against the current

d = 113.4 mi the distance of the travel against the current (in each direction)

t2 = the time of the return trip traveling with the current

the speed of the ship traveling with the current is: v + c

the speed of the ship traveling against the current is: v - c

since speed = distance/time follows distance = speed*time

traveling with the current:

(v + c)*t1 = d

(v + 1.9)*9 = 113.4 divide both sides by 9

v + 1.9 = 113.4/9

v = 113.4/9 - 1.9

traveling against the current:

(v - c)*t2 = d

(v - 1.9)*t2 = 113.4

by solving the system of equations:

v = 113.4/9 - 1.9

(v - 1.9)*t2 = 113.4

we find:

t2 = 12.89 hr

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

the ship needs 12.89 hours to return.