Respuesta :
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
