*****HELP PLEASE****?

Question

A riverboat takes tourists from St Louis up the Mississippi River 72 miles to Clarksville. The trip up the river takes 6 hours, and the return downstream takes 2 hours less time. What is the speed of the current and what is the speed of the riverboat.

PLEASE SHOW YOUR WORK. I'M TRYING TO WRAP MY BRAIN AROUND THESE PROBLEMS. THANK YOU IN ADVANCE

Answer 1

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The trip up the river has a speed of 72miles / 6 hours = 12mph.

The trip downstream has a speed of 72 miles / 4 hours = 18mph.

Let c be the speed of the current and let b be the speed of the boat.

The trip to St.Louis is going against the current. Thus, b - c = 12mph.

The trip back is going with the current. Thus, b + c = 18mph.

Now, add the two equations:

b - c = 12mph

b + c = 18mph

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2b = 30mph

b = 15mph

b + c = 18mph

15mph + c = 18mph

c = 3mph

Therefore, the speed of the current is 3mph and the speed of the boat is 15mph.