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A man started on a walk 12 km.
After walking half the distance at x km/h, he decreased his speed by 1/2 km/h.
He completed his walk 10 minutes later than he would have done if he had not decreased his speed.
Obtain an equation for x and solve it.
x = speed during the 1st 6 km
(x-.5} = speed during the last 6 km
Change 10 min to
Write a time equation: Time = dist/speed
6 km at normal speed + 6 km at slower speed = 12 km at normal speed + 10 min
Multiply equation by 6x(x-.5), results:
6(6(x-.5) + 6(6x) = 12(6(x-.5) + x(x-.5)
36(x-.5) + 36x = 72(x-.5) + x^2 - .5x
36x - 18 + 36x = 72x - 36 + x^2 - .5x
Combining like terms gives us:
0 = x^2 - .5x - 18
This will factor
(x + 4)(x - 4.5) = 0
x = 4.5 km/hr
Use your value of x to determine the time he took for the 12 kilometre walk.
Check solution by finding the time if 12 km walked at 4.5 km/hr