SOLUTION: A child can get to school in 15 minutes if she rides her bike. It takes her 45 minutes if she walks. Her speed when walking is 10 km./hr. slower than her speed when riding. How far

Question 75172: A child can get to school in 15 minutes if she rides her bike. It takes her 45 minutes if she walks. Her speed when walking is 10 km./hr. slower than her speed when riding. How far does she travel to school?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=her speed (rate) riding
Then x-10=her speed (rate) walking
distance(d)=rate(r) times time(t)or d=rt; r=d/t; t=d/r

We are told that time required to bike to school=15 min or 0.25 hr
We are also told that time required to walk to school =45 min or 0.75 hr
distance walking = distance riding
distance walking=rate walking times time walking
distance walking=(x-10)*0.75
distance riding = rate riding times time riding
distance riding =x*0.25
So our equation to solve is:
0.75(x-10)=0.25x get rid of parens
0.75x-7.5=0.25x subtract 0.25x and add 7.5 to both sides
0.75x-0.25x-7.7+7.5=0.25x-0.25x+7.5 collect like terms
0.50x=7.5 divide both sides by 0.50
x=15mph-speed (rate) riding
Now we have the rate and the time, so it's easy to get the distance
distance riding = rate times time (riding)
distance riding = 15*0.25=3.75 mi-------------------------------------ans
x-10=15-10=5mph-speed (rate) walking
distance walking = rate times time (walking)
distance walking = 5*0.75=3.75 mi-------------------------also the ans

hope this helps---------------ptaylor

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