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Brown Bag PS Solutions – Set A
#1 Augie Races the Train
Augie wants to catch a train that leaves at 10:45 A.M. and must ride his
bike to the station, which is 6 miles away. The first 2 miles are uphill,
the next 2 miles are flat, and the last 2 miles are downhill. Augie can
ride at 2 miles per hour (MPH) going uphill, 3 MPH on level ground,
and 4 MPH going downhill. He figures his average speed will be 3
MPH, so he plans to leave his house at 8:40 A.M. He thinks he will then
have five minutes to lock his bike and get on the train. Will he catch the
train? Why or why not? Show your work using words, numbers, and/or
pictures.
Solution
No. It takes Augie 1 hour to ride the first section, 40 minutes to ride the middle section, and 30
minutes for the downhill for a total of 130 minutes, or 2 hours and 10 minutes. If Augie leaves
at 8:40 A.M., he will not arrive until 10:50 A.M., 5 minutes after the train has left the station.
#2 Horse Problem
A man buys a horse for 50 dollars. Decides he wants to sell his horse
later and gets 60 dollars. He then decides to buy it back again and paid
70 dollars. However, he could no longer keep it and he sold it for 80 dollars.
Did he make money? lose money? or break even?
Explain why. Show your work using words, numbers, and/or pictures.
Solution
The answer to this one is that the man saw a 20 dollar profit. Whether
you use a number line or a debit/credit approach, the answer is $20.00 profit.
When presenting problems like this one to students or individuals, let them devise a plan for
solving the problem. Some students will need to act out the problem, others will need to draw
charts or graphs and then some individuals will work it out using various computations. Thinking skills are skills needed for a lifetime, by letting students devise their own plans and strategies in problem solving, they are improving their thinking skills. Although the solution seems
obvious, you will be amazed at the different answers.
Brown Bag PS Solutions – Set A
#3 Handshake Problem Problem of the Week
At the conclusion of a party, a total of 28 handshakes were exchanged.
Assuming that each person was equally polite toward all the others,
how many people were present?
Show your work using words, numbers, and/or pictures.
#4
Solution
8 people. This is the classic handshake problem worked backward.
Recommend method is to solve a simpler problem by setting up a table
and looking for a pattern. For example: 2 people
1 handshake;
3 people
3 handshakes; 4 people
6 handshakes; 5 people
10 handshakes; 6 people
15 handshakes; 7 people
21 handshakes;
8 people
28 handshakes.
#4 Locker Problem
There is a school with 100 students, and correspondingly 100 lockers,
all of which start off closed. The first student opens every locker.
The second student closes every other locker, starting with the second.
The third student changes the state of every third locker, starting with
the third. That is, if the locker is open, she closes it, and if it is closed,
she opens it. This continues similarly until all 100 students have passed
along the lockers.
After the 100th student is done, which lockers are open and which are
closed?
Show your work using words, numbers, and/or pictures.
Solution
The square numbered lockers (1, 4, 9...) are open, and all others are closed
n
2
3
4
5
6
7
8
Handshakes
1
3
6
10
15
21
28
Brown Bag PS Solutions – Set A
#5 Box of Chocolates
A decadent box of chocolates adorned the kitchen counter. When Jake
saw it, he ate 1/6 of the box. Then along came Joe and he ate 1/5 of
what Jake left. Along came Jill who ate 1/4 of the chocolates that remained. Later that day, Jeff ate 1/3 of the remaining chocolates.
By the time I got there, I managed to eat 1/2 of what remained. When
my sister Sandy came along, only 4 chocolates remained in the box.
Just how many chocolates did Jake manage to eat?
Show your work using words, numbers, and/or pictures.
Solution
4
Before Jake ate any of the chocolates, there were 24, he ate 1/6 of 24 which means he ate 4
which left 20 and Joe ate 1/5 of 20 which means he ate 4 which left 16 and Jill ate 1/4 meaning
she ate 4 which left 12, then Jeff ate 1/3 of 12 which means he ate 4. Leaving 8, then I came
and ate 1/2 of the 8 remaining, which means I ate 4 and left 4.