Middle School

1) Susan can type 4 pages of text in 10 minutes. Assuming she types at a constant rate, write the linear equation that represents the situation.

2) Phil can build 3 birdhouses in 5 days. Assuming he builds birdhouses at a constant rate, write the linear equation that represents the situation.

3) Train A can travel a distance of 500 miles in 8 hours. Assuming the train travels at a constant rate, write a linear equation that represents the situation.

4) Natalie can paint 40 square feet in 9 minutes. Assuming she paints at a constant rate, write the linear equation that represents the situation.

5) Bianca can run 5 miles in 41 minutes. Assuming she runs at a constant rate, write the linear equation that represents the situation.

6) Geoff can mow an entire lawn of 450 square feet in 30 minutes. Assuming he mows at a constant rate, write the linear equation that represents the situation.

(Try to answer all of them by writing a linear equation for each situation.)

Answer :

1) pages per minute is the rate. the rate is the slope pages/minutes = .4
y=.4x or y=2/5(x)
2)birdhouses per day is the slope. = .6
y=.6x or y=3/5(x)
3) miles per hour is the slope. 500/8=62.5
y=62.5x
4) square feet per minute is the slope. 40/9 =4.444444444
y=4.4444444444x or y=40/9(x)
5)miles per minutes is the rate. 5/41 is the slope.
y=5/41(x)
6) the rate is square feet per minute. 450/30=15
y=15x

Final answer:

The problem sets are solved by determining the rate at which each person or entity completes their task, then translating that rate into a linear equation. In all cases, the y-intercept is assumed to be 0 since no initial value is given.

Explanation:

In each of these scenarios, we need to calculate the constant rate and write it as a linear equation. Linear equations generally follow the form y = mx + b, where 'm' is the slope or rate, and 'b' is the y-intercept or initial value. However, for these problems, we can assume that the starting point or 'b' is 0 since we are not given an initial value.

  1. For Susan, the rate of typing is 4 pages/10 minutes or 0.4 pages per minute. The linear equation would be y = 0.4x.
  2. For Phil, the rate of building birdhouses is 3 birdhouses/5 days or 0.6 birdhouses per day. The linear equation would be y = 0.6x.
  3. For train A, the rate of traveling is 500 miles/8 hours or 62.5 miles per hour. The linear equation would be y = 62.5x.
  4. For Natalie, the rate of painting is 40 square feet/9 minutes or about 4.44 square feet per minute. The linear equation would be y = 4.44x.
  5. For Bianca, the rate of running is 5 miles/41 minutes or about 0.12 miles per minute. The linear equation would be y = 0.12x.
  6. For Geoff, the rate of mowing is 450 square ft/30 minutes or 15 square feet per minute. The linear equation would be y = 15x.

Learn more about Linear Equations here:

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