Challenge Problems

Wednesday, 28 April

(5 points) You MUST show work!

It takes two gardeners 8 days to mow a lawn.

One is lazy and one is energetic.

The energetic one would only take 12 days to mow it on his own.

How many days would the lazy gardener take to mow the lawn on his own?

Solution:

The energetic gardener would be able to mow the lawn in twelve days. In eight days he would be able to mow 8/12 of the lawn.

This leaves 4/12 of the lawn left for the lazy gardener to mow. He takes the full eight days to do this so he mows only half as quickly as the energetic one.

He would therefore need 24 days to mow the lawn on his own.
Twice as long as the energetic one.

Winner: Carlota De Armas

Tuesday, 27 April

Find three consecutive odd integers whose sum is 369.

(3 points)

Answer:

121, 123, 125

Winners: Marta S., Paula G. and Carlota D.A.

Friday-Monday, 23-26 April

Unit Fraction Problem

Find seven different unit fractions whose sum is 1. In other words, determine the values for a, b, c, d, e, f, and g in the following equation:

where a, b, c, d, e, f, and g are all different positive integers.

(5 points)

Solution to Problem:

2   6   8   12   20   24   30

or

3   5   6   8   10   20   40

or

2   4   8   16   36   48   72

or

2   4   8   16   32   34   544

or

3   4   6   9   13   18   156

or

3   5   6   9   12   18   20

or

3   4   7   8   14   24   28

Wednesday, 21st April

When the Workers Relax

Seven workers, Amie, Benny, Carol, David, Eric, Franklin, and Grace have a day off every week, no two of them on the same day.

You are told that Amie’s day off is the day after Carol’s;
that David’s day off is 3 days after the day before Eric’s;
that Benny’s day off is 3 days before Grace’s;
that Franklin’s day off is half way between Benny’s and Carol’s;
and that Franklin’s day off is Thursday.

Which day off does each worker have?

(4 points)

DAY OFF	WORKER
Sunday	Amie
Monday	Eric
Tuesday	Benny
Wednesday	David
Thursday	Franklin
Friday	Grace
Saturday	Carol

Tuesday, 20th April

In an isosceles triangle with vertices labeled A, B, and C, side AB is twice as long as side AC. If the perimeter is 200 meters, how long is side BC?

Hint: In an isoceles triangle two sides are equal.

(3 points)

Answer: 80 meters

Winner: Paula Gago

Challenge Problems:  19th April

Problem 1

The Math Teacher’s Fish  (5 points)

When Mr. Lowe returned from his fishing trip, his students inquired as to the length of his prize catch.
Mr. Lowe answered,
“The head measured 9 inches.”
“The tail was as long as the head and half the body.”
“The body was as long as the head and tail.”

How long was Mr. Lowe’s prize fish?

Solution:

1. Let H, B, and T be three variables representing the Head, Body, and Tail of the fish.
2. H = 9″.
3. T = H + 1/2 B
4. B = H + T
5. So, B = 9 + 9 + 1/2 B, by substitution.
6. Therefore, B = 36″.
7. So, T = 9 + 18 = 27″.
8. The Fish = H + B + T or 72″ in length.

Problem 2

(3 points)

Terry’s restaurant offers a 7-½ % discount for senior citizens. If a group of seniors paid $52.18 for lunch after the discount, what would they have paid without the discount?

Answer  $56.41

Problem 3

(2 points)

Al’s father is 45. He is 15 years older than twice Al’s age. How old is Al?

Answer:

Twice Al’s age is 2 x 15:	30
15 more than 30 is 15 + 30:	45

Wednesday, 24 & Thurday, 25

The 100 Meter Race Problem

A Sherando boy and a Handley girl ran a 100 meter race. The Handley girl crossed the finish line when the Sherando boy had gone 95 meters, so she won the race by 5 meters.
When they raced a second time, the Handley girl wanted to make the contest more even so she handicapped herself by starting 5 meters behind the start line.

If the two ran at the same constant speed as before, who won the second race? Explain (or give their times relative to each other).

(6 Challenge  points) To the first 5 students of each group to publish the correct answer in the blog.  Post your answer here!!!!!

Solution to Problem:

The Handley girl runs 100 meters in the same time that the Sherando boy runs 95 meters; therefore, the rate of the girl is 100 meters per some unit of time and the rate of the boy is 95 meters per the same unit of time.
Below is the Rate-Time-Distance table for the second race:

Runner	Rate	Time	Distance
Boy	95 m/unit	100/95 units	100 m
Girl	100 m/unit	105/100 units	105 m

So the Boy’s time is 100/95 or 1.05266316 units of time, and the Girl’s time is 105/100 or 1.05 units of time. Therefore, the Handley Girl won the second race as well! She passed the Sherando Boy at 95 meters

Monday, 22 March & Tuesday, 23 March

LOOK FROM DIFFERENT PERSPECTIVES!!!!

In this 4×4 grid of circles, how many different sets of four circles form the corners of a square (of any size)? One such set is shaded for you.

(4 Challenge  points) To the first 5 students of each group to publish the correct answer in the blog.  Post your answer here!!!!!

Answer: 20

Friday, 19 March

There are 7 secondary schools in the town of Newtonville.  Each school has a different total number of 1º ESO students.  School A has three fewer students than school B; school B has three fewer than school C; school C has three fewer than school D; school D has three fewer than school E; school E has three fewer than school F; school F has three fewer than school G.  If there are 2037 1º ESO students in the town of Newtonville, how many 1º ESO students are in the school with the least amount of 7th graders?

(5 Challenge  points) To the first 5 students of each group to publish the correct answer in the blog.  Post your answer here!!!!!

Answer: 282 Students

Winner: Paula Gago

Thursday, 18 March 2010

1. Jennifer wants to buy a new hockey puck that costs 5.25€. She has 2.30€. She can earn 50 cents an hour by raking leaves. How many hours will she have to work to get the money she needs?

(3 Challenge  points) To the first 5 students of each group to publish the correct answer in the blog.

Answer: 6 hours

Winner: Erik Déniz and Lorena

Wednesday, 17 March 2010

{7 + 4 · 3 – [(-2)² · 2 - 6)]}+ (2² + 6 – 5 · 3) + 3 – (5 – 2³ : 2) =

Answer: 14

Winner: Marta Sangrá

(3 Challenge  points) To the first 5 students of each group to publish the correct answer in the blog.  Post your answer here!!!!!

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Monday, 15 March 2010

Answer: 221195/512

No winners

(3 Challenge  points) To the first 5 students of each group to publish the correct answer in the blog.