Answer: The speed of the motorboat in still water is 45mph
The current rate is 9mph.
Step-by-step explanation:
Let u be the motorboat speed in still water and v be the current rate.
The effective speed going upstream is
Distance÷Time = 108÷3 = 36mph
It is the DIFFERENCE of the motorboat speed in still water and the rate of the current. It gives you your first equation
u - v = 36. (1)
The effective speed going downstream is
Distance÷Time = 108÷2 = 54mph
It is the SUM of the motorboat speed in still water and the rate of the current. It gives you your second equation
u + v = 54. (2)
Thus you have this system of two equations in 2 unknowns
u - v = 36, (1) and
u + v = 54. (2)
Add the two equations. You will get
2u = 36 + 54 = 90 ====> u = 90÷2 = 45mph
So, you just found the speed of the motorboat in still water. It is 45mph
Then from the equation (2) you get v = 54 = 45 = 9mph is the current rate.
Answer. The speed of the motorboat in still water is 45mph
The current rate is 9mph
