Can someone please help me with two math problems?(algebra 2)?

I've tried to get the right answer for these two problems but my teacher tells me that she won't count it right until i get the right answers can someone help me, please?

1. A cruise boat travels 48 miles downstream in 2 hours and returns upstream in 12 hours. Find the rate of the stream.

2.How many liters of a 30% alcohol solution must be mixed with 90 liters of a 60% solution to get a 40% soultion?Set up a system of linear equations and solve.

~thank you.

3 Answers

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  • Anonymous
    1 decade ago
    Favorite Answer

    Distance = Rate * Time

    d = rt

    1. A cruise boat travels 48 miles downstream in 2 hours and returns upstream in 12 hours.

    Let b = rate of boat, c = rate of current

    down:

    1) 48 = (b + c)2

    48 = 2b + 2c

    24 = b + c

    24 - c = b

    up:

    2) 48 = (b - c)12

    48 = 12b - 12c

    4 = b - c

    4 + c = b

    Equate the two expressions for b

    4 + c = 24 - c

    c = 20 - c

    2c = 20

    c = 10

    2.How many liters of a 30% alcohol solution must be mixed with 90 liters of a 60% solution to get a 40% soultion?Set up a system of linear equations and solve.

    If x = liters of 30% solution, then x + 90 is the liters of the final solution

    Add the concentrations to get the final

    .30x + .60(90) = .40(x + 90)

    .30x + 54 = .40x + 36

    - .10x = - 18

    x = 180

    check

    .30(180) + 54 = .40(270

    54 + 54 = 108

    108 = 108

  • 1 decade ago

    Q1. Say speed of boat is x miles/hour and stream is y miles/hour. You then get two equations;

    x+y=(48/2)=24 miles/hour and

    x-y=(48/12)=4 miles/hour

    now substituting x=4+y (from the 2nd equation) into the 1st equation you get;

    4+y+y=24 therefore 2y=20 -> y=10 miles/hour

    substituting this back into equation 2, you get x=4+10=14 miles/hour

    You only need to find the rate of the stream which was y and state the direction.

    Q2. Say x is litres of 30% solution

    30*x+60*90=40*(x+90) rearranging you get

    60*90-40*90=40*x-30*x

    90*(60-40)=x*(40-30)

    90*20=x*10

    therefore

    x=180 Litres

    Too check you would have 180L of 30% which is 54L of alcohol added to 54L of alcohol from the 60% solution (worked out from 60% of 90L). So in total you have 108L of alcohol in 270Litres of solution which is 108/270 = 0.4 = 40% concentration.

  • deeraj
    Lv 4
    4 years ago

    enable the 1st extensive sort be "x" the subsequent even extensive sort is "x+2" (x) + (x+2) = 118 2x + 2 = 118 2x = 118 - 2 = 116 x = 116 / 2 = fifty 8 There for, 2nd extensive sort is fifty 8 + 2 = 60 ===================================

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