a boat travels 12 miles up the river in the same amount of time it takes to travel 32 miles down the same river. if the current is 5 miles per hour, what is the speed of the boat in still water?



Answer :

Answer:

  11 mi/h

Step-by-step explanation:

You want the speed of the boat when it travels 12 miles upstream against a current of 5 mph in the same time it travels 32 miles downstream with the current.

Time

The relation between time, speed, and distance is ...

  time = distance/speed

If b represents the speed of the boat, the times upstream and downstream are the same, so we have ...

  (12 mi)/(b -5) = (32 mi)/(b+5)

Multiplying by the product of the denominators gives ...

  12(b+5) = 32(b-5) . . . . . . also divided by "mi"

  12b +60 = 32b -160 . . . . multiply by (b+5)(b-5)

  220 = 20b . . . . . . . . . . . . add 160 -12b

  11 = b . . . . . . . . . . . . . . . . . divide by 20

The speed of the boat in still water is 11 miles per hour.

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Additional comment

Each trip took 2 hours.