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During the first part of a trip, a canoeist travels 69 miles at a certain speed. The canoeist traveled 23 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2 hrs. What was the speed on each part of the trip?

  • algebra -

    1st part 69m @ X+5mph
    2nd part 23m @ X
    so,69m/x+5 + 23m/x = 2hours
    69/x+5 + 23/x = 2
    LCD ==> 69(x)+ 23(x+5)= 2x(x+5)
    69x+23x+115=2x^2+10x
    92x+115=2x^2+10x
    0=2x^2-82x-115
    wont factor, use quadratic formula
    x=(-b}ã(b^2-4ac))/2a
    x=-(-82)}ã(-82)^2 -(4)(2)(-115) / 2(2)
    +82 = 39.55mph, -82 = negative number
    so, 23 miles @ 39.55mph and 69 miles
    @ (39.55 + 5mph =) 44.55mph

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