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Math Help - rates and word questions

  1. #1
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    rates and word questions

    1.
    It takes 40 labourers to harvest a land of area 9600 m2 in 12 hours time. How many labourers it would take to harvest 17600 m2 of land in 10 hours?

    Method:

    I assumed that 40L harvested 9600 / 12 (9600 m2 per 12 hours)
    Then how many XL would it take to harvest 17600 / 10 (17600m2 per 1o hours)

    XL = (40 x 17600/10) x (12 / 9600) = 88 labourers’

    Any feedback on this method?

    2.

    If 48 Kg of cake can fill up 9 boys for a mountain hike of 4 hours, then how many hours of hiking can 120Kg of cake fill up 15 boys?

    Method:

    9 boys consume 48 Kg / 4 hours

    Then 15 boys will consume how much 120Kg/ X hours

    Number of hours = 9 x 120 x 4 / 48 x 15 = 6 hours.

    Any feedback on this method?
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  2. #2
    MHF Contributor

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    Quote Originally Posted by nazz View Post
    1.
    It takes 40 labourers to harvest a land of area 9600 m2 in 12 hours time. How many labourers it would take to harvest 17600 m2 of land in 10 hours?

    Method:

    I assumed that 40L harvested 9600 / 12 (9600 m2 per 12 hours)
    Then how many XL would it take to harvest 17600 / 10 (17600m2 per 1o hours)

    XL = (40 x 17600/10) x (12 / 9600) = 88 labourers’

    Any feedback on this method?
    It might be better to take it more "slowly", one step at a time rather than writing it as one big multiplication. 88 is more than 7 times as many workers as 12. 7 time 9600
    If it takes 40 laborers to to harvest a land of area 9600 m2 in 12 hours time then, assuming they all work at the same rate (or getting an average rate) each completes at 9600/40= 240 square meters in 12 hours and so 240/12= 20 square m per hour. To do 17600 m at that rate would take one worker 17600/20= 880 hours. To do it in 10 hours would require 880/10= 88 workers, exactly what you got.

    2.

    If 48 Kg of cake can fill up 9 boys for a mountain hike of 4 hours, then how many hours of hiking can 120Kg of cake fill up 15 boys?

    Method:

    9 boys consume 48 Kg / 4 hours

    Then 15 boys will consume how much 120Kg/ X hours

    Number of hours = 9 x 120 x 4 / 48 x 15 = 6 hours.

    Any feedback on this method?
    Cake for hiking? Wouldn't protein be better?
    Again, it would be better to say what each step is rather than just writing one long computation.
    48 kg of cake amoung 9 boys is 48/9= 16/3 kg per boy. Lasting 4 hours, that is (16/3)/4= 4/3 kg per boy per hour. Now go back the other way. 120 kg divided by 4/3 kg/(boy hour), in order to cancel "kg" is 90 boy-hours. Divided among 15 boys that is 90/15= 6 hours. The 120 kg will last 5 boys 6 hours.

    Both of your answers is correct so you "method" is correct. I would only say that your "method" is not stated very clearly. Especially if you are turning this in as homework, it would be better to explain each step.
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  3. #3
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    thanks for the feedback great help
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