SOLUTION: A cyclist travels from A to B, a distance of 8km, at x km/h. He travels from B to A the same distance, at x-4 km/h. If the total time taken is 1hour 10minutes, find x.

Question 512091: A cyclist travels from A to B, a distance of 8km, at x km/h. He travels from B to A the same distance, at x-4 km/h. If the total time taken is 1hour 10minutes, find x.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A cyclist travels from A to B, a distance of 8km, at x km/h.
He travels from B to A the same distance, at x-4 km/h.
If the total time taken is 1 hour 10minutes, find x.
:
Change 1 hr, 10 min to hr
:
write a time equation; time = dist/speed
:
AB time + BA time = hrs
+ =
Multiply by 6x(x-4), results:
6(x-4)*8 + 6x(8) = 7x(x-4)
48(x-4) + 48x = 7x^2 - 28x
48x - 192 + 48x = 7x^2 - 28x
96x - 192 = 7x^2 - 28x
0 = 7x^2 - 28x - 96x + 192
7x^2 - 124x + 192 = 0
you can use the quadratic formula to find x, but this will factor to:
(7x - 12)(x - 16) = 0
the reasonable answer
x = 16
:
:
See if that works out by finding the time each way
= .5 hrs
.667 hrs
---------------------
total 1.167 hrs, which is 1 hr 10 min

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