How do you do this one?
Almir can seal a driveway in 4 hours. Working together, he and Louis can seal it in 2.3 hours. How long would it take Louis to seal it working alone?
Thanks in advance.
D:3+4D=19
Driveway (D) = Rate * Time
let Louis' time alone be t hours
so Louis' rate is D/t
Almir's rate is D/4
their combined rate is D/2.3
so D/4 + D/t = D/2.3
divide by D,
1/4 + 1/t = 1/2.3
2.3t + 9.2 = 4t
I got t=5.411 hours
So Louis' rate alone is 5.4 Hours
thanks!
Well, Louis must be a really slow worker if it takes him 5.4 hours to seal a driveway on his own! Maybe he's just taking his time to make sure it's done perfectly. But hey, at least he's got Almir to help speed things up. Sealing a driveway can be a real pain, so it's always good to have a buddy...even if it means you have to share the credit (and the workload!).
To solve for Louis' time to seal the driveway working alone, we can set up an equation based on the given information.
Let's use the variable t to represent Louis' time in hours.
Using the formula: Rate * Time = Work, we can express each person's rate in terms of the time taken to seal the driveway:
Louis' rate = D/t, where D is the driveway, and t is the time taken by Louis.
Almir's rate = D/4, where D is the driveway, and 4 is the time taken by Almir.
Their combined rate working together is D/2.3, where D is the driveway and 2.3 is the time taken by both Louis and Almir together.
By adding up their individual rates, we get:
D/4 + D/t = D/2.3
To solve this equation, let's multiply through by 4 * 2.3t to get rid of the denominators:
2.3t * (D/4) + 4 * t * (D/t) = 4 * 2.3t * (D/2.3)
Simplifying:
2.3t * D/4 + 4 * D = 4 * t * D
Dividing through by D:
2.3t/4 + 4 = 4t
Multiply through by 4 to eliminate the fraction:
2.3t + 16 = 16t
Rearranging the terms:
16t - 2.3t = 16
13.7t = 16
Dividing both sides by 13.7:
t = 16/13.7
After evaluating this expression, we find that t is approximately 1.1686 hours.
Therefore, it would take Louis approximately 1.17 hours, or 1 hour and 10 minutes, to seal the driveway working alone.
To solve this problem, we can use the concept of rates and combined rates. Let's break it down step by step:
1. Let's assume Louis takes t hours to seal the driveway alone. Louis' rate of work is the amount of the driveway he can seal in 1 hour, which is D/t (D is the total driveway size).
2. Similarly, Almir takes 4 hours to seal the same driveway. Almir's rate of work is D/4.
3. When working together, their combined rate of work is D/2.3 (since they can seal the driveway in 2.3 hours when working together).
4. Now, we can set up an equation based on their rates of work: D/4 + D/t = D/2.3.
5. To solve the equation, we can clear the fractions by multiplying through by the least common multiple of the denominators, which is 4t * 2.3. This gives us:
(2.3)D + (4)D = (4t)D/2.3
6. Simplifying the equation, we get:
2.3D + 4D = 4tD/2.3
7. Combining like terms, we have:
6.3D = 4tD/2.3
8. Dividing both sides by D/2.3, we get:
6.3 = 4t
9. Finally, solving for t, we have:
t = 6.3/4
t ≈ 1.575
Therefore, it would take Louis approximately 1.575 hours to seal the driveway working alone.