Gene can proofread 3 essays in 1.7 hours. Working with his daughter Lauren, they can proofread 2 essays in 0.75 hours. Using a rational equation, which of the following correctly calculates how long it would take Lauren to proofread 1 essay by herself?

Question

1. 1.11 hours
2. 0.90 hours
3. 1.275 hours
4. 2.45 hours

Answer 1

Let L be the amount of time it takes for Lauren to proofread 1 essay by herself.
Considering their individual rates, we can set up the equation: 1/L + 1/1.7 = 1/0.75.
Multiplying through by L*1.7*0.75, we get 1.7*0.75 + L*0.75 = L*1.7.
Simplifying the left side gives 1.275 + 0.75L = 1.7L.
Subtracting 0.75L from both sides, we get 1.275 = 0.95L.
Dividing both sides by 0.95 gives L ≈ 1.34.
Therefore, it would take Lauren approximately 1.34 hours to proofread 1 essay by herself.

The correct answer is not among the options given.