Respuesta :
Answer:
Rate of current is 3 miles per hour and speed of the boat in still water is 7 miles per hour.
Step-by-step explanation:
This question is incomplete; find the complete question here.
A boat travels 20 miles upstream in 5 hours. Going downstream, it can travel 50 miles in the same amount of time. Find the speed of the current and the speed of the boat in still water.
Let the speed boat in the still water = x miles per hour
and the speed (rate) of the current = y miles per hour
Speed of the boat to go upstream (against the current) will be = (x - y)miles per hour
Since boat takes 5 hours downstream to travel 50 miles then from the formula,
[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]
[tex]5=\frac{50}{(x+y)}[/tex]
(x + y) = 10 -------(1)
Boat takes 5 hours to travel 50 miles upstream then,
[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]
5 = [tex]\frac{20}{(x-y)}[/tex]
x - y = 4 -----(2)
By adding equation (1) and question (2)
(x + y) + (x - y) = 14
2x = 14
x = 7 miles per hour
From equation (1),
7 + y = 10
y = 3 miles per hour
Therefore, Rate of current is 3 miles per hour and speed of the boat in still water is 7 miles per hour.
