Let's analyze the problem step-by-step to find the necessary work and power for both Blake and Sandra, and then compare them.
### Step 1: Calculate the work done by Blake
Blake drags 3 boxes, each with a force of 20 newtons over a distance of 10 meters. The work done (W) is given by the formula:
[tex]\[ W = F \times d \][/tex]
For Blake:
[tex]\[ W_{\text{Blake}} = 3 \times 20 \times 10 = 600 \text{ joules} \][/tex]
### Step 2: Calculate the work done by Sandra
Sandra drags 4 boxes, each with a force of 15 newtons over a distance of 12 meters. So, the work done is:
[tex]\[ W_{\text{Sandra}} = 4 \times 15 \times 12 = 720 \text{ joules} \][/tex]
### Step 3: Calculate the power for Blake
Power (P) is defined as work done per unit time:
[tex]\[ P = \frac{W}{t} \][/tex]
For Blake, taking 2 minutes (which is 120 seconds):
[tex]\[ P_{\text{Blake}} = \frac{600}{2} = 300 \text{ watts} \][/tex]
### Step 4: Calculate the power for Sandra
Sandra takes 4 minutes (which is 240 seconds) to do her work:
[tex]\[ P_{\text{Sandra}} = \frac{720}{4} = 180 \text{ watts} \][/tex]
### Step 5: Compare the work and power
- Blake does 600 joules of work.
- Sandra does 720 joules of work.
- Therefore, Sandra does more work than Blake.
- The power for Blake is 300 watts.
- The power for Sandra is 180 watts.
- Therefore, Blake's power is greater than Sandra's power.
### Conclusion
Blake does less work than Sandra. Blake's power is greater than Sandra's power.
