SOLUTION: A truck traveled the first 90 miles of a trip at one speed and the last 80 miles at an average speed of 5 miles per hour less. The entire trip took 4 hours. What was the average sp

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Question 534938: A truck traveled the first 90 miles of a trip at one speed and the last 80 miles at an average speed of 5 miles per hour less. The entire trip took 4 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 90 miles
second part 80 miles

speed in first part x mph
speed second part x -5 mph
Total rowing time 2 hours
Time first part 90 / x
Time second part 80 / ( x -5 )

Time first part + time second part = 4 hours

90 / x + 80 /(x -5 ) = 2
LCD = ( x + 0 )* (x -5 )
multiply the equation by the LCD
we get
90 * (x -5 )+ 80 x = 2
90 x -450 + 80 x = 2 X^2
180 x -450 = 2 X^2
2 X^2 -180 x 450 = 0
2 X^2+ -180 x+ 450 =
/ 2
1 X^2 -90 x 225 =
Find the roots of the equation by quadratic formula
a= 1 b= -90 c= 225
b^2-4ac= 8100 - -900
b^2-4ac= 7200
sqrt%28%097200%09%29= 84.85

x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 90 + 84.85 )/ 2
x1= 87.43 87 3/7
x2=( 90 -84.85 ) / 2
x2= 2.57 2 4/7
Ignore negative value
x = 87.43 mph LCD = speed

CHECK
Time first part + Time second part
1.03 + 0.97 = 2


m.ananth@hotmail.ca