1. Imelda, Susan, and Clara are driving go-carts around a track. Imelda takes 14 minutes, Susan takes 9 minutes, adn Clara takes 10 minutes to drive one lap. Suppose all three of them start together at a point and drive at their same speeds. After how many minutes will all three meet again?
2. How many squares with sides that are 6 inchess long are needed to cover a square with a side length of 30 inches without overlapping?
For the first one, we just need to find the least common multiple for 9, 10 and 14,,,,so we have
9 = 32
10 = 2 * 5
14 = 2 * 7
So the least common multilple is 32 * 2 * 5 * 7 = 630. And they will meet agiain in 630 minutes = 10.5 hrs.!!! (Hope they don't run out of gas!!)
For the second one....there will 5 rows of 5 squares each = 25 squares. To see this, note that the area of the big square = 900sq in. And the area of each little square = 36sq in So, 900/36 = 25 !!
1) To find when 14, 9, and 10 all meet, find the lowest common multiple:
14 = 2 x 7
9 = 3 x 3
10 = 5 x 2
Lowest common multiple = 2 x 7 x 3 x 3 x 5 = 630 minutes
2) It takes 5 squares of 6" each to reach 30"
Since there will 5 squares in both directions, it will take 25 squares.
Another way to solve the problem: 30" x 30" square is a total of 900 sq inches
Each square is 6" x 6" = 36 square inches.
Divide 900 sq in by 36 sq in to get 25 squares
For the first one, we just need to find the least common multiple for 9, 10 and 14,,,,so we have
9 = 32
10 = 2 * 5
14 = 2 * 7
So the least common multilple is 32 * 2 * 5 * 7 = 630. And they will meet agiain in 630 minutes = 10.5 hrs.!!! (Hope they don't run out of gas!!)
For the second one....there will 5 rows of 5 squares each = 25 squares. To see this, note that the area of the big square = 900sq in. And the area of each little square = 36sq in So, 900/36 = 25 !!