1) Carol and Claudia started at sunrise and each walked at constant speed. Carol

Question

1) Carol and Claudia started at sunrise and each walked at constant speed. Carol went from A to B, Claudia from B to A. They met at noon, and continuing with no stop, arrived respectively at B at 4:00 pm and at A at 9:00 pm. At what time was the sunrise? Explain and show ALL WORK!

2)You have four coins, each of which weighs either 9 grams or 10 grams (they could all be 9s, or three 9s and a 10, or ...). You also have an accurate scale, which will tell how many grams the items you put on it weigh. How can you determine the weight of each coin (i.e., all four of them) with just three weighings?

3)A basketball player early in the season had a free-throw percentage (the fraction she made out of the shots attempted) of less than 80%.  Later in the season her percentage had improved to more than 80%.  Must there have been a time during the season at which her percentage was exactly 80%? You have to justify your answer, of course.

Explanation / Answer

2)

weigh 3 of them , call them x1,x2,x3 ...so you get x1+x2+x3 = c ,where 27<=c<=30

Now weigh x3 and x4 =d...18<=d<=20

NOw weigh x2 and x4 = e ..18<=e<=20..

subtracting eqn 2 and 3 ,..

Now x3-x2 =d-e (known)

add it to eqn 1...

you get

x1+2x3=c+d-e

Now c+d-e is either of 27,28,29,30

now you obtain the value of x1 and x3 based on k=c+d-e ..

if k=30 impilies x1= 10 and x3 =10

if k =29 implies x3=10 and x1=9

if k=28 implies x3=9 and x1=10

if k=27 implies x3=9 and x1=9

once you have x3 get x4 from 2nd equation

and get x2 from 1st or 4th equation...

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