Question

Orlena can shovel the driveway in 6 hours, but if her sister Trinity helps it would take 4 hours. How long would it take Trinity to shovel the driveway alone?

Answer 1

If Orlena can shovel the driveway in 6 hours and if her sister Trinity helps, they can finish the job in 4 hours, then it would take Trinity 12 hours to shovel the driveway alone.

Step-by-step explanation:

Let's assume that Orlena can shovel the driveway alone in x hours. If Orlena can shovel the driveway in 6 hours, then her work rate is 1/6 of the driveway per hour. When Trinity helps, they can finish the job in 4 hours, so their combined work rate is 1/4. Therefore, Trinity's work rate is 1/4 - 1/6 = 1/12. To find out how long it would take Trinity to shovel the driveway alone, we need to calculate Trinity's work rate when working alone. Trinity's work rate is 1/x and is equal to 1/12. By multiplying both sides of the equation by 12x, we get x = 12.

Answer 2

Trinity would take approximately 3 hours and 50 minutes to shovel the driveway alone.

Step-by-step explanation:

To find how long it would take Trinity to shovel the driveway alone, we can set up a ratio based on the information given.

Let's assume Orlena's rate of shoveling is 'o' and Trinity's rate is 't'.

We can set up the equation as: 1/o + 1/t = 1/4 (since together they take 4 hours to shovel the driveway).

Simplifying the equation, we get: t + o = 4

Since we know Orlena's rate is 6, we can substitute it into the equation: t + 1/6 = 4

Subtracting 1/6 from both sides gives us: t = 4 - 1/6 = 23/6

Therefore, it would take Trinity 23/6 hours to shovel the driveway alone, which is approximately 3.83 hours or 3 hours and 50 minutes.