SOLUTION: A cyclist travels 80km from Paris to Louvre at an average speed of x km/h. Find the time taken in term of x. On his return journey from Louvre to Paris, he decreases his average sp

Question 205892: A cyclist travels 80km from Paris to Louvre at an average speed of x km/h. Find the time taken in term of x. On his return journey from Louvre to Paris, he decreases his average speed by 3km/h. Find the time taken on the return journey in terms of x. If the difference between the times is one hour 20 minutes, find the value of x.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A cyclist travels 80km from Paris to Louvre at an average speed of x km/h. Find the time taken in term of x.
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t1 = 80/x hours
- - - - -
On his return journey from Louvre to Paris, he decreases his average speed by 3km/h. Find the time taken on the return journey in terms of x.
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t2 = 80/(x-3) hours
- - - - -
If the difference between the times is one hour 20 minutes, find the value of x.
t1-t2 = 4/3 hours
80/x - 80/(x-3) = 4/3
Multiply thru by x(x-3)*3
80*(x-3)*3 - 80x*3 = 4x*(x-3)
240x-720 - 240x = 4x^2-12x
4x^2-12x+720 = 0
x^2-3x+180 = 0
(x-15)*(x+12) = 0
x = -12 kph (Ignore)
x = 15 khp
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