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

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Question 205971: 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 ankor@dixie-net.com(22740) About Me  (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.
f(x) = 80%2Fx
;
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.
f(x) = 80%2F%28%28x-3%29%29

If the difference between the times is one hour 20 minutes, find the value of x.
:
Write a time equation: 20 min = 1%2F3 hr
:
slow speed time - fast speed time = 20 min
80%2F%28%28x-3%29%29 - 80%2Fx = 1%2F3
multiply equation by 3x(x-3), results
3x(80) - 3(x-3)*80 = x(x-3)
:
240x - 240x + 720 = x^2 - 3x
Arrange as a quadratic equation
x^2 - 3x - 720 = 0
We have to use the quadratic formula here:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in this problem a=1; b=-3; c=-720
x+=+%28-%28-3%29+%2B-+sqrt%28-3%5E2+-+4+%2A+1%2A+-720+%29%29%2F%282%2A1%29+
:
x+=+%283+%2B-+sqrt%289+-+%28-2880%29+%29%29%2F2+
:
x+=+%283+%2B-+sqrt%289+%2B+2880%29%29%2F2+
:
x+=+%283+%2B-+sqrt%282889%29%29%2F2+
We want the positive solution here:
x = %283+%2B+53.6656%29%2F2
x = 56.6656%2F2
x = 28.33 km/hr
:
;
Check solution, find the times
80/25.33 = 3.16 hrs
80/28.33 = 2.82
---------------
differs = .34 hr ~ 20 min