Question

You are taking a typing class and can now type 30 words per minute. a. Set up a proportion to solve for the amount of time it would take you to type 400 words. b. Solve the proportion in part (a). c. Set up a proportion to solve for the number of words you could type in 10 minutes. d. Solve the proportion in part (c).

Answer 1

To determine the time required to type 400 words at 30 words per minute, set up a proportion and solve it to find that it takes approximately 13.33 minutes. For the number of words typed in 10 minutes, set up a different proportion to find that you could type 300 words in that time.

Step-by-step explanation:

To determine how long it would take to type 400 words at a speed of 30 words per minute, you set up a proportion where the number of words goes on the top and the time in minutes goes on the bottom. The proportion for part (a) would look like this: 30/1 = 400/x, where x represents the time in minutes required to type 400 words.

To solve the proportion for part (b), cross-multiply to get 30x = 400, and then divide both sides by 30 to find x. Through this calculation, x = 400/30, which simplifies to approximately 13.33 minutes.

For part (c), you set up a different proportion to find out how many words can be typed in 10 minutes. This proportion looks like: 30/1 = w/10, where w represents the number of words you could type in 10 minutes.

To solve the proportion for part (d), cross-multiply to get w = 300. This means you could type 300 words in 10 minutes.

Answer 2

To find the time to type 400 words at 30 words per minute, set up the proportion 30/1 = 400/x and solve for x, giving 13.33 minutes. To find how many words you can type in 10 minutes, set up the proportion 30/1 = y/10 and solve for y, resulting in 300 words.

Step-by-step explanation:

Setting up and Solving Proportions

To determine how long it would take to type 400 words at a rate of 30 words per minute, we need to set up a proportion. A proportion is an equation that states two ratios are equivalent.

Part a: Setting up the proportion

If you type 30 words per minute, then a proportional rate for x minutes to type 400 words can be set up as:

30 words/1 minute = 400 words/x minutes.

Part b: Solving the proportion

By cross-multiplication, we solve for x: (30 words) * (x minutes) = (400 words) * (1 minute). This simplifies to 30x = 400, thus x = 400/30, which equals 13.33 minutes.

Part c: Setting up another proportion

Now, to find out how many words you can type in 10 minutes, we set up another proportion based on the original rate: 30 words/1 minute = y words/10 minutes.

Part d: Solving the second proportion

Again using cross-multiplication: (30 words) * (10 minutes) = (1 minute) * (y words), which gives 300 = y.

So, you can type 300 words in 10 minutes.