Answer: the speed of the boat in still water is 13 mph.
the current of the river is 3 mph
Step-by-step explanation:
Let x represent the speed of the boat in still water.
Let y represent the current of the river.
The boat travels between two cities that are 18 miles apart.
When going downstream, with the current, the trip takes 9/8 hour(s). The total speed of the boat would be (x + y) mph
Distance = speed × time
Distance travelled while going downstream is
18 = 9/8(x + y)
18 = 1.125(x + y)
Dividing both sides by 1.125, it becomes
16 = x + y - - - - - - - - - - 1
Returning upstream, against the current, the boat covers the same distance in 9/5 hour(s). The total speed of the boat would be (x - y) mph. Distance travelled while going upstream is
18 = 9/5(x - y)
18 = 1.8(x - y)
Dividing both sides by 1.8, it becomes
10 = x - y - - - - - - - - - - 2
Adding equation 1 to equation 2, it becomes
26 = 2x
x = 26/2 = 13
Substituting x = 13 into equation 2, it becomes
10 = 13 - y
y = 13 - 10
y = 3
