SOLUTION: I have been given a very challenging word problem and cannot figure it out. It's on Finding rates. Jeff bicycles 160 miles at the rate of r mph. The same trip would have taken 2

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Question 742968: I have been given a very challenging word problem and cannot figure it out. It's on Finding rates. Jeff bicycles 160 miles at the rate of r mph. The same trip would have taken 2 hours longer if he had decreased his speed by 4 mph. Find r. Can you please help me solve this problem?...thanks
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
d=160
speed = r
t=160/r

d=160
new speed = r-4
t= 160/(r-4)

time new speed time original speed = 2
160%2F%28r-4%29-160%2Fr=2

multiply by r(r-2)
160r-9600+160r= 2r(r-4)

320r-9600=2r^2-8r
2r^2-328r+9600=0
/2
r^2-164r+4800=0
r^2-164r+6724=6724-4800
(r-82)^2=1924
r-82=43.86
r=82-43.86
r=38.14