Three scientists are observing Rickey and Riley, laboratory rats, to see how long each rat takes to find a piece of cake in a maze. The maze is a large box with open pathways running north-south and east-west in a grid pattern. Riley takes the direct route by traveling three rows north, turning right and traveling two columns east, proceeding four rows north and turning right for one column. He is one row south of the cake when the bell goes off. Rickey, on the other hand, fumbles his way along. He enters at the same gate as Riley and advances twelve rows north. He then becomes confused and does an about-face, and moves eight rows south along the same path. Then he moves left one column and north one row. Finally he makes a right turn and moves four columns to the east. How far away from the cake is Rickey if the bell goes off at this point?
Well, it seems like Rickey really took the scenic route, didn't he? Let's calculate his distance from the cake.
Rickey starts by going 12 rows north and then goes 8 rows south. So, effectively, he's gone 12 - 8 = 4 rows north.
Then he moves left one column and north one row. This means he has moved 1 column to the west and 1 row to the north.
Finally, Rickey makes a right turn and moves four columns to the east.
So, if we sum up all his movements, Rickey is 4 rows north, 1 column west, and 4 columns east from where he started.
Now, let's see where Riley is to figure out how far Rickey is from the cake. Riley traveled 3 rows north, turned two columns east, went four rows north, and then turned right.
Well, well, well! Look at that! Rickey and Riley are in the same spot! So, if the bell goes off at this point, Rickey is right next to Riley, and they are both one row south of the cake.
Now, let's hope those rats don't eat all the cake before the scientists can reach it!
To determine how far away Rickey is from the cake when the bell goes off, we need to calculate his final position in the maze.
Let's break down Rickey's movements step by step:
1. Rickey enters the maze and travels 12 rows north.
2. Rickey becomes confused and moves 8 rows south along the same path.
3. Rickey moves left one column and north one row.
4. Rickey makes a right turn and moves 4 columns to the east.
Now, let's calculate Rickey's final position:
1. Rickey initially moves 12 rows north. Since each row represents a distance of 1, he is now 12 rows north.
2. Rickey then moves 8 rows south. This cancels out the previous movement, so he is now back at 0 rows north.
3. Rickey moves left one column and north one row. This means he is now one column to the left (west) and one row up.
4. Finally, Rickey makes a right turn and moves 4 columns to the east. This brings him back to the same column he started in, but now he is four columns to the east.
In summary, Rickey's final position is 0 rows north and 4 columns east from where he entered the maze.
However, we need to compare this to Riley's position, who was one row south of the cake when the bell went off. Therefore, Rickey is one row south and four columns east from the cake.
To determine how far away Rickey is from the cake when the bell goes off, we need to follow the directions given for Rickey's movements in the maze.
1. Rickey enters at the same gate as Riley and moves twelve rows north.
2. Rickey becomes confused and moves eight rows south along the same path.
3. Rickey moves left one column and north one row.
4. Finally, Rickey makes a right turn and moves four columns to the east.
Let's break down Rickey's movements step by step:
1. Starting at Riley's position (three rows north and two columns east), Rickey moves twelve rows north. This puts him at the same north-south row as Riley, but twelve rows north.
2. Rickey then becomes confused and moves eight rows south along the same path. This cancels out his previous movement and brings him back to the same row as Riley, but now only four rows north.
3. Rickey moves left one column. Since the maze is in a grid pattern with open pathways running north-south and east-west, moving one column to the left means subtracting one from the east-west position (columns). This brings him one column west of Riley.
4. Rickey moves north one row. This brings him to the same north-south row as Riley, but one row north.
5. Finally, Rickey makes a right turn and moves four columns to the east. Starting from his current position (one row north and one column west of Riley), moving four columns to the east means adding four to the east-west position (columns). This brings him three columns east of Riley.
Considering all the movements, Rickey is now three rows north and three columns east of Riley. Since Riley is one row south of the cake, Rickey is two rows north of the cake. Therefore, Rickey is two rows away from the cake when the bell goes off.
Well, why not just sketch a grid and do what each of the rats do ?
I am sure you can follow the steps just as well as any of us.
I suggest you make the origin your starting point.
It easy to see that Riley ends up at (7,3) with the cake at (7,4)
Do the same for the other rat