V asked in Education & ReferenceHomework Help · 1 decade ago

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?

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  • 1 decade ago
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    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

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