Answer :
To find out how long it takes Monica to paint both canvases, we need to consider the areas of the canvases and the fact that she paints at a constant rate. Let's break it down step by step:
1. Calculate the Area of Each Canvas:
- The first canvas measures 25 inches by 20 inches. Its area is:
[tex]\[
\text{Area of first canvas} = 25 \times 20 = 500 \text{ square inches}
\][/tex]
- The second canvas measures 20 inches by 15 inches. Its area is:
[tex]\[
\text{Area of second canvas} = 20 \times 15 = 300 \text{ square inches}
\][/tex]
2. Determine the Relationship Between Painting Times:
- Let [tex]\( t \)[/tex] represent the time it takes Monica to paint the second canvas (300 square inches).
- It takes Monica 20 minutes longer to paint the first canvas than the second canvas. Therefore, the time to paint the first canvas is [tex]\( t + 20 \)[/tex].
3. Set Up the Equation:
- Since Monica paints at the same rate, we set the rates equal to each other:
[tex]\[
\frac{500}{t + 20} = \frac{300}{t}
\][/tex]
- This equation states that the rate of painting the area of the first canvas is equal to the rate of painting the area of the second canvas.
4. Solve for [tex]\( t \)[/tex]:
- Solving the equation [tex]\( 500 \times t = 300 \times (t + 20) \)[/tex] gives us [tex]\( t = 30 \)[/tex] minutes for the second canvas.
5. Calculate the Time for the First Canvas:
- Since it takes 20 minutes longer for the first canvas, the time is [tex]\( 30 + 20 = 50 \)[/tex] minutes.
6. Find the Total Time for Both Canvases:
- Adding the times for both canvases gives us:
[tex]\[
\text{Total time} = 30 + 50 = 80 \text{ minutes}
\][/tex]
Therefore, it takes Monica 80 minutes to paint both canvases. The correct answer is C. 80 minutes.
1. Calculate the Area of Each Canvas:
- The first canvas measures 25 inches by 20 inches. Its area is:
[tex]\[
\text{Area of first canvas} = 25 \times 20 = 500 \text{ square inches}
\][/tex]
- The second canvas measures 20 inches by 15 inches. Its area is:
[tex]\[
\text{Area of second canvas} = 20 \times 15 = 300 \text{ square inches}
\][/tex]
2. Determine the Relationship Between Painting Times:
- Let [tex]\( t \)[/tex] represent the time it takes Monica to paint the second canvas (300 square inches).
- It takes Monica 20 minutes longer to paint the first canvas than the second canvas. Therefore, the time to paint the first canvas is [tex]\( t + 20 \)[/tex].
3. Set Up the Equation:
- Since Monica paints at the same rate, we set the rates equal to each other:
[tex]\[
\frac{500}{t + 20} = \frac{300}{t}
\][/tex]
- This equation states that the rate of painting the area of the first canvas is equal to the rate of painting the area of the second canvas.
4. Solve for [tex]\( t \)[/tex]:
- Solving the equation [tex]\( 500 \times t = 300 \times (t + 20) \)[/tex] gives us [tex]\( t = 30 \)[/tex] minutes for the second canvas.
5. Calculate the Time for the First Canvas:
- Since it takes 20 minutes longer for the first canvas, the time is [tex]\( 30 + 20 = 50 \)[/tex] minutes.
6. Find the Total Time for Both Canvases:
- Adding the times for both canvases gives us:
[tex]\[
\text{Total time} = 30 + 50 = 80 \text{ minutes}
\][/tex]
Therefore, it takes Monica 80 minutes to paint both canvases. The correct answer is C. 80 minutes.
