Question 266295: sue can ride bike 14 km/h faster than she can walk
it takes 17.5 min longer to walk 2.5 km than to ride. find sue's walking speed Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Ler r=Sue's rate of speed walking
Then r+14 =her rate of speed biking
time required to ride 2.5km=(2.5)/(r+14)
time required to walk=(2.5)/r
So, our equation to solve is:
(note: 17.5 min=17.5/60 hr--and we are dealing in hours)
(2.5)/r-(17.5)/60=(2.5)/(r+14) multiply each term by 60*r*(r+14)
(2.5)(60)(r+14)-17.5r(r+14)=(2.5)(60)r simplify
150r+2100-17.5r^2-245r=150r subtract 150r from each side
`150r-150r+2100-17.5r^2-245r=150r-150r collect like terms
-17.5r^2-245r+2100=0 divide each term by -17.5
r^2+14r-120=0 Quadratic in standard form and it can be factored
(r-6)(r+20)=0
r=6 km/hr------------------her rate of speed walking
r=-20 km/hr-----------------------disregard. rates in this case are positive
x+14=6+14=20 km/kr her rate of speed biking
CK
2.5/6-17.5/60=2.5/20
-17.5/60=7.5/60-25/60
-17.5/60=-17.5/60
Hope this helps---ptaylor
