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

RELATED QUESTIONS
Respected sir, 1] A train travelling 25km an hour leaves Delhi at 9 a.m. & another... (answered by ejazali_syed)

A man walks a certain distance at a certain rate. Had he walked 1/2 km per hour faster,... (answered by ankor@dixie-net.com)

A man walk a certain distance at certain rate. Had he walked 1/2 km an hour faster he... (answered by ankor@dixie-net.com)

A boy at 8:00 A.M. started to walk at the rate of 4 km/hr for 2 hours and 45 minutes,... (answered by ankor@dixie-net.com)

a field is 90 m by 70 m.A man walks round in at the rate of 4 km. per hour. What time... (answered by josmiceli)

need to write an equation and solve Julia Ling drove the 200 km to Richmond at a speed (answered by ikleyn)

A man walks a certain distance with certain speed. If he walks a1/2 km an hour faster, he (answered by josgarithmetic,MathTherapy)

a boy rides a bicycle at a certain rate for 5 km then decreases his rate by 2 km per hour (answered by josgarithmetic)

A boy rides a bicycle at a certain rate for 5 km then decreases his rate by 2 km per... (answered by josgarithmetic)