Sarah had 4 pieces of rope.each piece was twice the length of the previous piece. the first piece was 1 foot 3 inches long. How many feet of rope did Sarah have altogether.
first piece=1 foot 3 inches
second piece= 2x1 foot 3 inches
third piece= 2 foot 6 inches x2
fourth piece=4 foot 12 inches
all the rope= 9 feet 24 inches
better check again. The pieces are
1'3"
2"6"
4'12"
8'24"
add them up. Or, using a geometric series, the total is 1.25(2^4-1) = 18.75
To find out how many feet of rope Sarah had altogether, we first need to convert all the measurements to the same unit, which is feet.
Let's start with the measurements given:
First piece = 1 foot 3 inches
To convert this to feet, we need to know that 1 foot is equal to 12 inches. Therefore, the first piece is 1 + (3/12) = 1.25 feet.
Second piece = 2 times 1 foot 3 inches
Since the first piece is 1.25 feet, the second piece is 2 * 1.25 = 2.5 feet.
Third piece = 2 times 2 feet 6 inches
To convert 2 feet 6 inches to feet, we have 2 + (6/12) = 2.5 feet. So the third piece is 2 * 2.5 = 5 feet.
Fourth piece = 4 feet 12 inches
To convert 12 inches to feet, we divide 12 by 12, which equals 1 foot. Therefore, the fourth piece is 4 + 1 = 5 feet.
Now, we can add up all the lengths of the four pieces of rope:
1.25 + 2.5 + 5 + 5 = 13.75 feet.
Therefore, Sarah had a total of 13.75 feet of rope altogether.