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pyz01
Lv 7
pyz01 asked in Science & MathematicsMathematics · 1 decade ago

Will they make it to the destination?

A construction company has a large pile of rocks that they need hauled 41 miles away. The company has no machines but has 75 men to haul the rocks. The 75 men can haul the rocks in one day's work about 5 miles. The average workload and rate is the same for all 75 men.

But, the wrinkle is that, after each day, 5 men must leave to go back to a different job. The foreman in charge asks you, a mathematician, if by losing 5 men each day, whether all the rocks will be moved the complete 41 miles. He also asks you, if the answer is no, how far will he miss so that he can figure out what to do to get to the full 41 miles.

What do you tell him? Remember, the foreman does not know math very well, so please explain and show him how/why you answered the way you did.

Update:

Note to Answers - don't forget the last two days add up to one more mile.

Update 2:

OK - I guess I will give this answerer best answer since he is the only one to answer. However, the answer is 40 miles and they will miss by 1 mile. Knowing that they will miss by only one mile, the foreman will keep the last 15 workers for two extra days.

1 Answer

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  • billrussell42
    Lv 7
    1 decade ago
    Favorite Answer

    I'll assume that after the 5 men leave, they don't come back.

    Call the total number of rocks N

    On the first day, the 75 men haul N rocks 5 miles. Each man can haul N/75 rocks 5 miles

    On the second day 70 men can haul (70/75)*N 5 miles, or all the rocks 4.667 miles.

    On the third day 65v men can haul 65/75 or 4.333 miles

    on the fourth day 60 men can haul 60/75 or 4.0 miles

    so se have a series:

    5, 4 2/3, 4 1/3, 4, 3 2/3, 3 1/3, 3, 2 2/3, 2 1/3, 2, 1 2/3, 1 1/3, 1, 2/3, 1/3, 0

    Adding them up, we get 5+13+10+7+4 = 39

    so they only reach 39 miles.

    .

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