SOLUTION: A track and field runner saves 1 hour by covering 112 km at a rate which is 2 km per hour faster than usual rate. How many hours does he usually take to travel this distance?
Question 953754: A track and field runner saves 1 hour by covering 112 km at a rate which is 2 km per hour faster than usual rate. How many hours does he usually take to travel this distance? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A track and field runner saves 1 hour by covering 112 km at a rate which is 2 km per hour faster than usual rate.
How many hours does he usually take to travel this distance?
:
let s = his normal running speed
then
(s+2) = his faster running speed
:
Write a time equation; time = dist/speed
normal time - faster time = 1 hr - = 1
multiply equation by s(s+2)
s(s+2)* - s(s+2)* = 1s(s+2)
Cancel the denominators
112(s+2) - 112s = s^2 + 2s
112s + 224 - 112s = s^2 + 2s
combine like terms on the right to form a quadratic equation
0 = s^2 + 2s - 224
factors to
(s+16)(s-14) = 0
The positive solution
s = 14 km/hr is the normal speed
find the normal time
112/14 = 8 hrs is the normal time
:
:
Confirm this by finding the time at the faster speed
112/16 = 7 hrs, 1 hr less
