SOLUTION: Nasser rode his bicycle 66 miles in 4.5 hours. for the first 40 miles he averaged a certain rate, and then for the last 26 miles he reduced his rate by 3 miles per hour. find his r

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Question 474398: Nasser rode his bicycle 66 miles in 4.5 hours. for the first 40 miles he averaged a certain rate, and then for the last 26 miles he reduced his rate by 3 miles per hour. find his rate for the last 26 miles.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Speed first part x mph
speed second part 3 mph less

First part 40 miles
Second part 26 miles

speed in first part x mph
speed second part x -5 mph
Total rowing time 4.5 hours
Time first part 40/x
Time second part 26/(x-5)

Time first part + time second part =4.5 hours

40/x+26/(x-5)=4.5
LCD =x* (x-5)
multiply the equation by the LCD
we get
40*(x-5 )+26x=4.5
40x-200 +26x=4.5X^2-22.5x
66x-200 =4.5x^2+200
4.5X^2-88.5x+200=0
4.5x^2 -88.5x+ 200=0
/4.5
x^2 -19.67 x +44.44 = 0

Find the roots of the equation by quadratic formula

a= 1 b= -19.67 c= 44.44

b^2-4ac= 386.78 - -177.78
b^2-4ac= 209
sqrt%28%09209%09%29= 14.46
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=( 19.67 + 14.46 )/ 2
x1= 17.06
x2=( 19.67 -14.46 ) / 2
x2= 2.6
Ignore x2 value not posssible
x = 17.06 mph
17.06-6 = 12.06 mph speed second part