SOLUTION: Hello,distance and time are not really my strong points... Winnie and Piglet decided to visit one another and set off at the same time to each others house. When they met on the r

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Question 1043954: Hello,distance and time are not really my strong points...
Winnie and Piglet decided to visit one another and set off at the same time to each others house. When they met on the road joining their houses, they forgot that they wanted to see each other and continued walking. Winnie reached Piglet's house 8 minutes after the meeting and Piglet got to Winnie's house 18 minutes after the meeting. How long did it take Piglet to reach Pooh's house from the time he left his own house?
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hello,distance and time are not really my strong points...
Winnie and Piglet decided to visit one another and set off at the same time to each others house. When they met on the road
joining their houses, they forgot that they wanted to see each other and continued walking. Winnie reached Piglet's house
8 minutes after the meeting and Piglet got to Winnie's house 18 minutes after the meeting.
How long did it take Piglet to reach Pooh's house from the time he left his own house?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let V%5Bw%5D be Winnie's speed and V%5Bp%5D be Piglet's speed.

Let t be the time from the start to the meeting moment.

Then you have these equations

V%5Bw%5D%2At = W%5Bp%5D%2A18,   (1)   and
V%5Bp%5D%2At = W%5Bw%5D%2A8.    (2)

It implies 

V%5Bw%5D%2FW%7Bp%5D = 18%2Ft,         (1')   ( from (1) ) and
V%5Bw%5D%2FV%5Bp%5D = t%2F8.          (2')   ( from (2) ).

Hence,  18%2Ft = t%2F8,  and then  t%5E2 = 18%2A8 = 144.

Therefore, t = sqrt%28144%29 = 12.

In other words, it took 12 minutes from the start to the meeting moment.

Then the total time for Piglet to reach Pooh's house was 12 + 18 minutes = 30 minutes.

Answer.  The total time for Piglet to reach Pooh's house was 12 + 18 minutes = 30 minutes.

This problem is very similar to that of the lesson
    - Another unusual Travel problem (Arnold's problem on two walking old women)
in this site.

For lessons on Travel and Distance consult
    - OVERVIEW of lessons on Travel and Distance
in this site.

You also have free of charge online Textbook in Algebra-I
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK
in this site.


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the speed with which Winnie walked and let represent the speed with which Piglet walked. The entire distance from Winnie's house to Piglet's house is and we can divide that distance into two pieces, , the distance from Winnie's house to the point where they met, and , the distance from Piglet's house to the same point. And we know that . Since we know they left at the same time, the time it took each of them to get to the meeting point is the same amount of time and we will call that .

Since we know that distance equals rate times time, we can now establish some relationships between the above variables.

The distance from Piglet's house to the meeting point can be expressed in two different ways:



because is Piglet's rate and is the time it took Piglet to get to the meeting point, and



because is Winnie's rate and it took Winnie 8 minutes to get to Piglet's house after the meeting point. But then we can say:



Similarly, considering the distance from Winnie's house to the meeting, we can come up with:



And now we have:



A little algebra gets us to:



Which is to say:



And now we know that Winnie walked one and one-half times as fast as Piglet.

Going back to an earlier relationship we had established:



Now substitute for



Now we know it took Piglet 12 minutes to get to the meeting place and 18 minutes to get from the meeting place to Winnie's house for a total of 30 minutes.

John

My calculator said it, I believe it, that settles it