THE MEETING POINT Because the spring comes with

feelings of good cheer and warmth, four

friends, Ana, Betty, Mara and Serena

decided to go to the park, located near the

school.

Mara, more affected by the spring

fatigue, hasnt been to school, but she

thought it would be better to breathe some

fresh air along with her friends. So, after

she picked up some chocolate bars just in

case and put them in her bag, she got out

as soon as she received the text message from Betty and Serena, who had already gone out of the

school yard. Mara walked slowly, knowing she is 300 m ahead, her block of flats being closer to

the park than the school. After 3 minutes and a half, she had already walked 200 m and she was

starting to feel anxious about the time of the meeting.

Serena went from school directly towards the park, but due to her back problems, she

decided to leave some

books in a drawer in the

classroom. In 4

minutes, she reached

the local shop, located

400 m away from the

school. In just 2

minutes, she bought

some juice, then she

began running towards

the meeting point when

she came in a minute.

Ana left from the

school too, but with a

delay of 3 minutes,

because she stopped to

borrow a book from the

schools library.

Because of this delay,

she had to go faster to

0

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700

800

0 1 2 3 4 5 6 7 8

Mara

Serena

Ana

Betty

t (min)

CCCllliiinnn SSSiiimmmeeessscccuuu 888 CCC

recover lost time, so in just 2 minutes, she has walked 350 m, very quickly reaching the shop

where Serena was waiting.

Betty, the poet of the group, left school with Serena, but the magnificent trees and the

beautiful scents have awakened her artistic sense, so she was hovering, gathering ideas, feelings

and pictures, that she is going to use in her next poems for the school magazine and other

literature contests. After 2 minutes, she was already 100 m away from the school and she didnt

even notice Serena, when she had gone pass the store where she was staying. Betty kept walking

until she reached 700 m in little over 7 minutes.

At one point, the girls met, and the story of their journeys were transposed into a coordinate

system by four graphs representing the distance each girl had traveled and their time, resolving the

project for their mathematics lesson. The meeting point, where the graphs intersect, can be seen

from the graph, but it can also be calculated.

First, we determine the linear functions shown in the figure.

We know that baxxf )( and ffGB

GA)500;5,3(

)300;0(

.By solving the system of equations,

5005,33000

baba it results that 300b and

7

400a .

So the straight blue line is the graph of the function 3007

400)( xxf . In the same way we

can calculate the other 2 functions.

For the green chart, we have 525175)( xxf . P (x ; y) is the intersection point of the two

graphs. From 5251753007

400xx we can say that x=7 and y=700.

Serena and Betty arrive in

7 minutes at the meeting point,

located 700 m from the school, so

the four friends had met at the

point P(7; 700) and a beautiful

adventure began there, in a

beautiful spring day in the park,

near the school.

Written in Romanian by

Dimciu Mara, translated into English by Cisu Dragos VIII C.