SOLUTION: On a recent trip, a trucker traveled 300 mi at a constant rate. Because of improved road conditions, the trucker then increased the speed by 10 mph. An additional 240 mi was travel

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Question 785722: On a recent trip, a trucker traveled 300 mi at a constant rate. Because of improved road conditions, the trucker then increased the speed by 10 mph. An additional 240 mi was traveled at the increased rate. The entire trip took 16 h. Find the rate of the trucker for the first 300 mi
Answer by mananth(16946) About Me  (Show Source):
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On a recent trip, a trucker traveled 300 mi at a constant rate. Because of improved road conditions, the trucker then increased the speed by 10 mph. An additional 240 mi was traveled at the increased rate. The entire trip took 16 h. Find the rate of the trucker for the first 300 mi
let the rate for first 300 miles be x m/h
speed increased to x+10 miles/h
d=rt
Total distance traveled = 540 miles

300/x + 240/(x+10) = 16
multiply by x(x+10)
300(x+10)+240x=16x(x+10)
300x+3000+240x=16x^2+160x
16x^2-380x-3000=0

Find the roots of the equation by quadratic formula

a= 16 , b= -380 , c= -3000

b^2-4ac= 144400 + 192000
b^2-4ac= 336400
%09sqrt%28%09336400%09%29=%09580%09
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=( 380 + 580 )/ 32
x1= 30
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 380 -580 ) / 32
x2= -6.25
Ignore negative value
Truc speed 30 mph

m.ananth@hotmail.ca