Answer: the speed of the current is 3 mph
Step-by-step explanation:
Let x represent the speed of the river's current.
The speed of the steamboat in still water is 11 miles per hour.
Traveling with the current the steamboat can travel 77 miles downstream. The total speed downstream would be
(11 + x) mph
In the same amount of time, the steamboat travels 44 miles upstream against the current. The total speed upstream would be
(11 - x) mph.
Time = distance/speed
The time spent travelling downstream is
77/(11 + x)
The time spent travelling upstream is
44/(11 - x)
Since the time is the same, then
77/(11 + x) = 44/(11 - x)
Cross multiplying, it becomes
77(11 - x) = 44(11 + x)
847 - 77x = 484 + 44x
44x + 77x = 847 - 484
121x = 363
x = 363/121
x = 3
