Can someone please help me with math?

If anyone can show me how to do these, it would be great.

1)Twin brothers, Andy and Brian, can mow their grandparents lawn together in 90 minutes. Brian can mow the lawn by himself in 19 minutes more than it would take Andy. How long would it take to each mow the lawn?

2) A boat travels 10 km upsteam and 10 km back. The time for the roundtrip is 9 hours. The speed of the stream is 5 km/h. What is the speed of the boat in still water?

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  • 7 years ago
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    1) Andy alone takes x minutes

    Brian alone takes ( x+19) minutes

    Andy alone in 1 minute does 1 /x of the job

    Brian alone in 1 minute does 1/ ( x+19) of the job

    Together in 1 minute they do ( 1/x + 1/ ( x+19) ) of the job

    Since together they take 90 minutes , in 1 minute they do 1/90 of the job

    1/x + 1/ ( x+19) = 1/90

    MULTIPLY BOTH SIDES BY 90x( x+19)

    90 ( x+19) + 90x = x ( x+19)

    90x + 1710 +90x = x^2 +19x

    x^2 - 161x - 1710 = 0

    x^2 + 10x - 171x -1710 = 0

    x ( x+10) -171 ( x + 10) = 0

    ( x-171) ( x+10) = 0

    Rejecting the negative value

    x = 171

    ANSWER Andy alone 171 minutes Brian = 190 minutes

    CHECK

    1/171 + 1/190 = 361/32490 = 1/90

    2) Let speed of boat in still waters be x km/ hour

    10/ (x+5) + 10/ ( x-5) = 9

    10 ( x-5) + 10( x+5) = 9 ( x+5) ( x-5)

    20x = 9x^2 - 225

    9x^2 -20x - 225 = 0

    9x^2 - 20x = 225

    DIVIDE BY 9

    x^2 - 20/9x = 225/9

    ADD 100/81

    x^2 -20/9x + 100/81 = 100/81 +225/9 = 2125/81

    ( x - 10/9) ^2 = 2125/81

    x = 1/9 ( 10 + \/2125 ) OR 1/9 ( 10 - \/2125 )

    Rejecting the negative value

    x = 6.233 km/ hour ANSWER

    CHECK

    10/ (6.233+5) = 10/11.233 = 0.89hours

    10/ ( 6.233-5) = 10/1.233 = 8.11 hours

    ADD = 9 hours

  • 7 years ago

    1) all you would do is subtract 90 - 19 and what you get is the total minutes that the other brother has.

    Ex. 90 - 19 = 71

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