Problem Solving help please!?
1) A boat can travel 24 mi in 3 h when traveling with a current. Against the same current, it can travel only 16 mi in 4 h. Find the rate of the current and the rate of the boat in still water.
2) In a mayoral election, the incumbent received 25% more votes than the opponent. Altogether, 5175 votes were cast for the two candidates. How many votes did the incumbent mayor receive?
- Seamus OLv 71 decade agoFavorite Answer
Let speed of boat in still water = x
Let speed of current = c
Speed of boat with current = x + c = 24/3 = 8
Speed of boat against current = x - c = 16/4 = 4
So x + c = 8 [eqn 1]
x - c = 4 [eqn 2]
[eqn 1] - [eqn 2] → 2c = 4
c = 2
Subs c = 2 into [eqn 1] → x + 2 = 8
x = 6
So rate of current is 2 mph and the rate of the boat in still water is 6 mph
2) Let number of opponents votes = x
Number of incumbents votes = 5175 - x
Incumbent received 25% more votes so 5175 - x = 1.25x
5175 = 2.25x
x = 2300
So incumbent got 5175 - 2300 = 2875 votes