Adrianas 18kilometer boat trip downriver took two hours but

Adriana\'s 18-kilometer boat trip downriver took two hours, but the return trip back upstream took three hours. Figure the speed of the boat in still water and the speed of the current of the river.

Solution

speed of the boat in still water= x km/h
speed of the current= y km/h
down stream speed=(x+y) km/h
up stream speed=(x-y) km/h
time=distance/speed
according to the problem
total distance=18 km
speed of the boat in down stream=(x+y) km/h
time taken down stream=2hours
distance/speed of down stream= 2h
18/(x+y)=2
multiplying by (x+y) on both sides
18
------ *(x+y)=2*(x+y)
(x+y)
18=2(x+y)
time taken up stream=3hours
distance/speed of upstream=3h
18/(x-y)=3
multiplying by (x-y) on both sides
18
------ *(x-y)=3*(x-y)
(x-y)
18=3(x-y)
2(x+y)=18
dividing by 2 on both sides
2(x+y)/2=18/2
x+y=9 -----(1) equation
3(x-y)=18
dividing by 3 on both sides
3(x-y)/3=18/3
x-y=6 ----(2) equation
solving 1 and 2 equations
x+y=9
x-y=6
------
2x=15
dividing by 2 on both sides
2x/2=15/2
x=7.5
substitute in 1 st equation
x+y=9
7.5+y=9
subtracting 7.5 on both sides
7.5+y-7.5=9-7.5
y=9-7.5
y=1.5
speed of the boat in still water=7.5 km/h
speed of current=1.5 km/h