A boat travels 50 mi upstream against the current in the same amount of time it takes to travel 70 mi downstream with the current. If the current is 3 mph what is the speed of the boat in still water

Answer: the speed of the boat in still water is 18 mph

Step-by-step explanation:

Let x represent the speed of the boat in still water.

If the current is 3 mph and the boat travels 50 miles upstream against the current, the total speed of the boat would be (x - 3) miles

Time = distance/speed

Time taken for the boat to travel 50 miles upstream is

50 / (x - 3)

In the same amount of time, the boat travels 70 miles downstream with the current. The total speed of the boat would be (x + 3) miles. Time taken for the boat to travel 70 miles upstream is

70 / (x + 3)

Since the time is the same, then

50 / (x - 3) = 70 / (x + 3)

Cross multiplying, it becomes

70 (x - 3) = 50 (x + 3)

70x - 210 = 50x + 150

70x - 50x = 150 + 210

20x = 360

x = 360/20

x = 18 mph