Question

A tugboat goes 100 miles upstream in 10 hours. The return trip downstream takes 5 hours. Find the speed of the tugboat without a current and the speed of the current.

The speed of the tugboat is ____ mph and the speed of the current is _____ mph

Answer 1

A tugboat goes 100 miles upstream in 10 hours. The return trip takes 5 hours. Find the speed of the tugboat without a current and the speed of the current.
:
let s = speed in still water
Let c = speed of the current
then
(s-c) = effective speed upstream
and
(s+c) = effective speed downstream
:
Write distance equation for each way. (dist = time * speed
10(s-c) = 100

5(s+c) = 100
Simplify both equations, divide the 1st equation by 10, divide the 2nd equation by 5, results:
s - c = 10
s + c = 20
-----------Adding eliminates c find s
2s = 30
s = 30/2
s = 15 mph boat speed in still water
:
You can find the current, check the solutions in the original equations

Answer 2

tugboat 15 mph . current 5 mph. let speed of boat is v1 and current v2. so upstream net speed = v1-v2 (opp. direction),. so dist.= speed *time. and downstream v1+v2 .solve v1 and v2. 2 eq.\[v1 + v2 = 20 ; v1 - v2= 10 ; \]

Answer 3

Thank you