Matt and Carla together can mow a lawn in 8 hours, alone Carla takes four times longer than Matt. How long does Matt take?
If Matt takes m hours, then Carla takes 4m. So, together,
1/m + 1/4m = 1/8
5/4m = 1/8
m = 10
To find out how long Matt takes to mow a lawn, we can follow these steps:
1. Let's assume that Matt takes x hours to complete mowing a lawn.
2. According to the problem, Carla takes four times longer than Matt. So, Carla takes 4x hours to complete mowing a lawn.
3. When Matt and Carla work together, they can mow a lawn in 8 hours. This means that their combined work rate is 1/8 of a lawn per hour.
4. Matt's work rate is 1/x of a lawn per hour. Similarly, Carla's work rate is 1/(4x) of a lawn per hour.
5. When we add Matt and Carla's work rates together, it should equal their combined work rate. So, we can write the equation as: 1/x + 1/(4x) = 1/8.
6. To solve this equation, we can find a common denominator for the fractions and combine them: (4 + 1)/(4x) = 1/8.
7. Simplifying the equation gives us: 5/(4x) = 1/8.
8. Cross-multiplying the equation results in: 5 * 8 = 1 * 4x.
9. Simplifying this equation gives us: 40 = 4x.
10. Dividing both sides of the equation by 4 results in: 10 = x.
Therefore, Matt takes 10 hours to mow a lawn.