A steamboat can travel at an average speed of 11 miles per hour in still water. Traveling with the current the steamboat can travel 77 miles down the river in the same amount of time it takes to travel 44 miles upstream against the current. Find the speed of the current.

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

18.75 gallons

step-by-step explanation: