a sailboat travels 20 miles in 3hrsit returns4hrs what is the speed the sailboat in still water&the rate curre

Question

a sailboat travels 20miles downstrean in 3hrs. it returns in 4 hrs. find the speed of the sailboat in still water and the rate of the current.

Answer 1

Please, explain to your teacher, that the speed of sailboat in still water cannot be found, beacuse the direction of the wind is unknown. This problem is easy to solve in case of motorboat, but not sailboat.

Answer 2

The speed of the sailboat in still water is s. The speed of the current is c. Therefore, the downstream velocity is s + c. The upstream velocity is s - c. The distance divided by the velocity gives the amount of time required for travel in each direction.

20 / (s + c) = 3
20 / (s - c) = 4

This is now a system of two equations in two variables, so we should be able to solve for both.

20 / (s + c) = 3 ==> 3s + 3c = 20
20 / (s - c) = 4 ==> 4s - 4c = 20 ==> s - c = 5 ==> s = 5 + c

3s + 3c = 20
3(5 + c) + 3c = 20
15 + 6c = 20
c = 5/6 mph or 0.83 mph (current)
s = 5 + c = 5 and 5/6 mph or 35/6 mph or 5.83 mph (sailboat in still water)

Answer 3

Let S= speed in still water and C is the current.
(S+C) x 3 = 20 miles downstream
(S-C) x 4 = 20 miles upstream.

You now have two equations and you can find two variables.

S+C=20/3
S-C=20/4
Add those equations and you get 2S = 20/3 + 20/4
so S = 10/3 + 10/4 = 40/12+30/12 = 70/12 = 5.83 mph

Now put that in the equation S+C=20/3
so you get C=20/3 - 70/12
C = 80/12 - 70/12 = 10/12 = .83 mph