Question

MP Model with Mathematics Serena estimates that she can paint 60 square feet of wall space every half-hour. Write an equation for the relationship with time in hours as the independent variable. Can Serena paint 400 square feet of wall space in 3.5 hours? Why or why not?

a. 60t=400, No, she cannot.
b. 120t=400, No, she cannot.
c. 60t=210, Yes, she can.
d. 120t=210, Yes, she can.

Answer 1

Serena can paint 120 square feet per hour. The equation for the relationship is S = 120t. Consequently, Serena can paint 400 square feet in 3.5 hours as 120 * 3.5 equals 420 square feet.

Step-by-step explanation:

Serena's painting rate is 60 square feet every half-hour. To write an equation for this relationship with time in hours as the independent variable, we first convert her rate to per hour by doubling it, since there are 2 half-hours in an hour. This means Serena can paint 120 square feet per hour. The equation relating the number of square feet painted (S) to the time in hours (t) is S = 120t.

Now, let's determine if Serena can paint 400 square feet in 3.5 hours. Using the equation, we calculate S = 120 * 3.5, which equals 420. Since 420 is greater than 400, Serena can indeed paint 400 square feet in 3.5 hours. Therefore, the correct answer is d. 120t=210, Yes, she can, although the correct equation should be 120t=400 to represent the situation accurately.