A boat can travel 114 miles upstream
in the same time that it can travel 186 miles downstream.
If the speed of the current is 6 miles per hour,
find the speed of the boat without a current.
2 answers
any help would be greatly appreciated :)
Speed of boat in still water = V mi/h.
Speed of boat upstream = V-6 mi/h.
Speed of boat down stream = V+6 mi/h.
(V-6)t = 114 mi.
Eq1: Vt - 6t = 114.
(V+6)t = 186 mi.
Eq2: Vt + 6t = 186.
Add Eq1 and Eq2 and get:
2Vt = 300,
Vt = 150.
In Eq1, substitute 150 for Vt:
150 - 6t = 114,
-6t = 114 - 150 = -36,
t = 6h.
In Eq2, substitute 6 for t:
6V + 6*6 = 186,
6V + 36 = 186,
6V = 150,
V = 25mi/h.
Speed of boat upstream = V-6 mi/h.
Speed of boat down stream = V+6 mi/h.
(V-6)t = 114 mi.
Eq1: Vt - 6t = 114.
(V+6)t = 186 mi.
Eq2: Vt + 6t = 186.
Add Eq1 and Eq2 and get:
2Vt = 300,
Vt = 150.
In Eq1, substitute 150 for Vt:
150 - 6t = 114,
-6t = 114 - 150 = -36,
t = 6h.
In Eq2, substitute 6 for t:
6V + 6*6 = 186,
6V + 36 = 186,
6V = 150,
V = 25mi/h.
1 answer