Final answer:
To find Ross's individual mulching time, we use the equation incorporating work rate, with Jake's rate as 1/35 and their combined rate as 1/18. The equation is 1/35 + 1/t = 1/18, where t is the time in minutes it takes for Ross to mulch the garden alone.
Step-by-step explanation:
To set up the rational equation for how long it will take Ross to mulch the garden by himself, we need to consider the work rates of Jake and Ross combined and individually. If Jake can mulch a garden in 35 minutes, his rate of working is 1 garden per 35 minutes, which we can write as 1/35 of a garden per minute. If Jake and Ross together can mulch the same garden in 18 minutes, their combined rate of working is 1 garden per 18 minutes, written as 1/18 of a garden per minute. We are looking for the time t, in minutes, that it takes for Ross to mulch the garden alone. To find this, we use the equation that expresses work rate: Jake's rate × minutes worked (which is 35) + Ross' rate × minutes worked (which is t) = 1 whole garden mulched. Therefore, the equation will be1/35 + 1/t = 1/18.