SOLUTION: A truck traveled the first 165 miles of a trip at one speed and the last 100 miles at an average speed of 5 miles per hour less. The entire trip took 5 hours. What was the average

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Question 809412: A truck traveled the first 165 miles of a trip at one speed and the last 100 miles at an average speed of 5 miles per hour less. The entire trip took 5 hours. What was the average speed for the first part of the trip?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
First Part x mph
Second Part x -5 mph
Total time 5 hours
First Part time 165 / x
Second Part time 100 / ( x -5 )

Time first part + time second part = 5 hours

165 / x + 100 /(x -5 ) = 5
LCD = ( x + 0 )* (x -5 )
multiply the equation by the LCD
we get
165 * (x+ -5 = 5
165 x+ -825 + )+ 100 x = 5 X^2 -25 x
290 x+ -825 = 5 X^2 = 0
5 X^2 -290 x+ 825 = 0
5 X^2+ -290 x+ 825 =
/ 5 0
5 X^2 -290 x+ 825 =
/5
x^2-58x+165=0
factors are -55 & -3
x=55 OR 3
first part 55 mph
second part =50 mph