Boat goes downstream 72miles in 3hrs & upstream 60miles in 6hrs, the rate of the river and the rate of the boat in still water respectively are??

River speed: The downstream leg equals 72/3 = 24 miles per hour
Boat speed: The upstream leg equals 60/6 = 10 miles per hour
Knowing the boat is traveling in 24mph water and moving upstream at 10mph the boat must be able to move 34mph in still water.

You posted this in the homework section. Please read the rules about asking homework questions, posted here:

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sleepingless, you would do well to also read those rules. We do not answer homework questions on this site. The poster was given this homework for a reason. Unless you plan to take the test for him, giving him the answer is not helpful, and that's what we aspire to on this site, helping.

Strange boat we have here, it can go faster in still water than it can down stream.

I see someone getting an F on this question.

What is the rate that the boat goes down stream?
What is the rate that the boat goes up stream?

r=\frac{d}{t}

How can you calculate the rate of the boat and stream?

r_{bu} + r_r = r_{bd} - r_r

Rate of the boat upstream + rate of the river = rate of the boat downstream - rate of the river

Solve for rate of the river...