SOLUTION: 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 h

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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 h      Log On


   

Question 288992: 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. Use your value of x to determine the time he took for the 12 kilometre walk.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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
then
(x-.5} = speed during the last 6 km
;
Change 10 min to 1%2F6 hr
:
Write a time equation: Time = dist/speed
:
6 km at normal speed + 6 km at slower speed = 12 km at normal speed + 10 min
6%2Fx + 6%2F%28%28x-.5%29%29 = 12%2Fx + 1%2F6
:
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
Positive solution
x = 4.5 km/hr
:
Use your value of x to determine the time he took for the 12 kilometre walk.
:
6%2F4.5 + 6%2F4 =
11%2F3 + 11%2F2 = 25%2F6 hrs
:
Check solution by finding the time if 12 km walked at 4.5 km/hr
12%2F4.5 = 24%2F6 hr, 1%2F6 hr faster