Amotorboat takes 3 hours to travel 108 mi going upstream. the return trip takes 2 hours going downstream. what is the rate of the boat in still water and what is the rate of the current?

1.rate of the boat in still water
2.rte of the current

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

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step-by-step explanation: