### Video Transcript

Catherine is planning to plant flowers in her flowerbed. Each flower needs to be planted in a square-shaped plot of earth with length 35 centimeters. She will plant them in a grid as shown below. The maximum length of the flowerbed is 2.3 meters. The maximum width of the flowerbed is 1.7 meters. Catherine is going to fill her flowerbed with as many flowers as possible. She can plant one flower every three minutes. Part a) Assuming that our flowerbed is in the shape of a rectangle, calculate how long it will take her to plant as many flowers as possible in her flowerbed.

This question does look incredibly intimidating. But if we break it down bit by bit, we will be just fine. We know the size of the plots for each of the flowers. Since these are square plots, they are 35 centimeters by 35 centimeters. We also know the length of the flowerbed to be a maximum of 2.3 meters and the width to be a maximum of 1.7 meters.

We need to work out how many flowers she can plant altogether in her rectangular flowerbed. Now, since the measurement for each plot is in centimeters and the dimensions of the flowerbed is in meters, we’ll need to convert the dimensions of the flowerbed into centimeters first.

One meter is equivalent to 100 centimeters. This means we can convert our measurements from meters into measurements in centimeters by multiplying them by 100. 2.3 multiplied by 100 is 230. So the maximum length of the flowerbed is 230 centimeters. 1.7 multiplied by 100 is 170, meaning that the maximum width of the flowerbed is 170 centimeters. We need to find the number of plots that will fit lengthwise and the number that will fit widthwise.

Since each plot has a length of 35 centimeters, we can divide 230 by 35. Essentially, we’re sharing that 230 centimeters into 35-centimeter plots. 230 divided by 35 is 6.57. We can’t have part of a plot for the flowers though. So we say that we can have six plots lengthways.

To work out the number of plots that will fit widthways, we divide 170 by 35; that’s 4.85. Once again, we can’t have a part of a plot. So we say that we have four plots widthways. So it’s a rectangular flowerbed with six plots lengthways and four plots widthways.

To find the total number of plots, that is, we multiply the number of plots in one row — that’s six — by the number of rows — that’s four. Six multiplied by four is 24 So there will be 24 plots for flowers. The only part of information we have yet to use is the time it takes her to plant one flower.

We’re told that one flower takes three minutes. We need to assume that the rate at which she plants the flowers is consistent; she doesn’t slow down or speed up. That means that two flowers would take six minutes, three flowers would take nine minutes, and so on.

We know she’s going to plant 24 flowers. We can then calculate the time taken to plant these 24 flowers by multiplying 24 by three; that’s 72. It takes her 72 minutes to plant all of her flowers.

Her flowerbed might not be in the shape of a rectangle. Part b) Explain how this could affect the time it will take for her to plant as many flowers as possible in her flowerbed.

If her flowerbed is not in the shape of a rectangle, it could be in a whole number of different shapes. It could even look something like this. If that’s the case, it might be that she can’t quite fit 24 plots for her flowers. If this was the case, there would be less plots. And therefore, it would take her less time to fill her flowerbed.