SOLUTION: an adult sets out from home to pick up their child from school, and walks at a pace that will take 10 minutes to get to the school. At exactly the same time,the child leaves school

Algebra ->  Proportions -> SOLUTION: an adult sets out from home to pick up their child from school, and walks at a pace that will take 10 minutes to get to the school. At exactly the same time,the child leaves school      Log On


   

Question 213793: an adult sets out from home to pick up their child from school, and walks at a pace that will take 10 minutes to get to the school. At exactly the same time,the child leaves school to walk home at a pace that will take 20 minutes to get home. After how long will they meet? How would you justify your solution to the child?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
an adult sets out from home to pick up their child from school,
and walks at a pace that will take 10 minutes to get to the school.
At exactly the same time,the child leaves school to walk home at a pace that
will take 20 minutes to get home.
After how long will they meet?
;
Let t = time interval when they walk towards each other
:
From the information given, we can say the adult walks twice as fast as the child
Let s = walking speed of the child
then
2s = walking speed of the adult
and
3s = their relative speed walking towards each other
:
Write a dist equation Dist = speed * time
:
Combined dist = child walking 20 min to home
3s(t) = 20s
divide both sides by s
3t = 20
t = 20%2F3
t = 62%2F3 min
or
Combined dist = adult walking 10 min
3s(t) = 10(2s)
3s(t) = 20t
divide both sides by s
3t = 20
t = 20%2F3
t = 62%2F3 min
:
How would you justify your solution to the child?
:
You can say since I walk twice as fast as you do, I will cover twice the
distance.
therefore
in 62%2F3 min, child covers 1%2F3 the dist
and
in 62%2F3 min, adult covers 2%2F3 the dist (twice as fast)