SOLUTION: `During the first part of a trip a canoeist travels 56 miles at a certain speed. the canoeist travels 9 miles on the second part of the trip at 5 mph slower. the total time for the

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Question 561044: `During the first part of a trip a canoeist travels 56 miles at a certain speed. the canoeist travels 9 miles on the second part of the trip at 5 mph slower. the total time for the trip is 5 hours. what was the speed on each part of the trip?''.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
first part 56 miles
second part 9 miles

speed in first part x mph
speed second part x-5 mph
Total rowing time3 hours
Time first part 56/x
Time second part 9/(x-5)
Time first part + time second part = 5 hours
56/x+9/(x-5)=5
LCD = x*(x-5)
multiply the equation by the LCD
we get
56*(x-5)+9x=5(x(x-5))
56x-280 +9x=5x^2+-25x
90x-280 =5x^2
5X^2-90 x+280 = 0
5 x^2+ -90 x+ 280 =
/ 5
x^2-18x+56
x^2-14x-4x+56=0
x(x-14)-4(x-14)=0
(x-14)(x-4)=0
first part speed = 14 mph
second part 14-5 =9 mph
m.ananth@hotmail.ca