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 (3)
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)
miles per hour is the slope. 500/8=62.5 y=62.5x
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)
the rate is square feet per minute. 450/30=15 y=15x
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. ;
Each scenario's linear equation is derived from finding the constant rate of work for each individual. For example, Susan's typing rate translates to the equation y = 0.4 x , while Bianca's running translates to y ≈ 0.12 x . All equations model a direct relationship between the time spent on the task and the amount completed.
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