Final answer:
Martin and Joey's combined rate of work is 8/15 of a yard per hour. To find out how long it would take for them to rake the yard together, divide one yard by their combined rate, resulting in 15/8 hours or 1 hour and 52.5 minutes.
Step-by-step explanation:
The question asks us to determine how long it would take Martin and Joey to rake a yard together if Martin can do it in 3 hours and Joey can do it in 5 hours. To solve this, we need to find their rates of work and then combine them to find their rate working together.
Martin's rate of work is 1 yard per 3 hours or ⅓ of a yard per hour. Joey's rate of work is 1 yard per 5 hours or ⅕ of a yard per hour. When working together, their rates add up, so the combined rate is ⅓ + ⅕ of a yard per hour.
To add fractions, we need a common denominator. The smallest common denominator for 3 and 5 is 15. So we convert each rate to have a denominator of 15:
- Martin: ⅓ = ⅓ × ⅕/⅕ = 5/15 of a yard per hour
- Joey: ⅕ = ⅕ × ⅓/⅓ = 3/15 of a yard per hour
Combined rate: 5/15 + 3/15 = 8/15 of a yard per hour.
Now, to find the total time it would take them working together to rake one yard, we divide 1 yard by their combined rate:
Time = 1 yard ÷ (8/15 of a yard per hour) = 15/8 hours
15/8 hours is equivalent to 1 hour and 52.5 minutes. Therefore, it would take Martin and Joey 1 hour and 52.5 minutes to rake the yard together.