Answer:
11 mi/h
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.