To write the rational equation for this problem, we first need to consider the work rates of Timmy, Marcos, and Meghan, and the fact that they are working together to mulch a yard.
Let x be the time it would take Meghan to mulch a yard by herself.
The work Timmy does in 1 hour is a fraction of the yard he can mulch by himself in 8 hours. So, Timmy's work rate is 1/8 of a yard per hour.
Likewise, Marcos can mulch a yard by himself in 7 hours, so his work rate is 1/7 of a yard per hour.
We don't know Meghan's work rate exactly, but we do know that she can complete a yard by herself in x hours. Thus, Meghan's work rate is 1/x of a yard per hour.
When they work together, they can mulch a yard in 2 hours. This means their combined work rate equals 1/2 yard per hour since they complete half a yard in 1 hour.
The sum of their individual work rates when they work together equals their combined work rate. Therefore, we can set up the rational equation as follows:
Timmy's work rate + Marcos's work rate + Meghan's work rate = Combined work rate
(1/8) + (1/7) + (1/x) = 1/2
This is the rational equation that represents the scenario, where x represents the time it would take Meghan to complete the mulching of a yard by herself. We do not solve for x at this stage, as the instruction is to just provide the rational equation.
