## Saturday, July 18, 2009

### One hectic summer morning

Summer is not easy on the working parents. Camps are usually further away from home than schools are, camps start later and end earlier than schools. So, go figure how to squeeze an 8-hour working day in-between...

Here is a puzzle inspired by my friend's real life story.
She lives 15 miles South from where she works.
Her son goes to a camp 10 miles West from home. She drops him off, then heads to work. As she is not able to pick her son from the camp at 4pm, she arranged a carpool with another family, that unfortunately lives in the opposite direction: 5 miles East from her. So, on a regular camp morning, my friend leaves her house early to pick up this other kid, then drives both kids to the camp and then continues to work. In addition to all this, on one morning last week she got a call from a friend from work. Friend had some car trouble and pleaded to be picked up on her way to work. Friend lives 2 miles South from my friend's home.
What is the minimum number of miles my friend had to travel on this hectic morning before reaching her work?

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Alin Grin said...

49

5 east and 5 back =10
10 West and 10 back =20
2 miles south and 2 back =4
And 15 miles to work.
10+20+4+15=49

rachel_t said...

First I made a little map and calculated the hypotenuse of the triangles. W=Work Location, C=Camp Location, H=Home Location, B=Son's Friend Location, F=Coworker's Location:

----------- W

------- / --- |

18.028 - 15mi

-- / -------- |

C - 10mi - H -- 5mi - B

-- \ -------- | ------- /

10.198 -- 2mi --- 5.385

------- \ --- | --- /

------------ F

Then I tried a few of the options that the driver could take.

1) Coworker's to son's friend to camp to work
= 2+5.385+5+10+18.028=40.413

2) Coworker's to son's friend to camp to work (Only driving N-S and E-W)
= 2+2+5+10+10+15=49

3) Son's friend, to Coworker's to Camp to work
= 5+5.385+10.198+18.028=38.611

4) Son's friend to camp to Coworker's to work
= 5+5+10+10.198+2+15=47.198

It looks like the way to drive the least would be to pick up son's friend, drive SW to coworker's, drive NW to camp, drive NE to work. Though, it's probably too optimistic that there'd be roads to make that work.

Maria said...

Rachel's solution is shorter.
As every experienced mom, my friend new that cutting some corners would save her time. And she probably new Pythagoras theorem.
It looks like drawings are not allowed in the comments of the blog, so I will make the drawing that Rachel was trying to do above and add it to the puzzle text.

Great job there, all the midnight puzzle solvers!

Maria said...

Maura MacK entered the following solution, but erroneosly in the different puzzle:

If the roads only run N/S and E/W, then she must drive a total of 49 miles this morning. H to B and back (10 miles) + H to F and back (4 miles) + H to C and back (20 miles) = H to W (15 miles) = 49.

However, if roads run along the hypotenuse of the triangles that can be superimposed on the diagram, then she would "only" have to drive 38.62 miles. She would follow this path: H to B (5 miles) + B to F (5.385 miles) + F to C (10.2 miles) + C to W (18.03) = 38.62.

Absolutely right, Maura!
I can't give the puzzle point to you as Rachel T already solved it first, but new puzzles are for grabs daily.