Final answer:
Justin and Jayme will both have candied the same number of apples after 5 hours. At that time, they will have a total of 70 candied apples together.
Step-by-step explanation:
Justin and Jayme are working at different rates to candy apples. The time taken for them to have the same number of candied apples can be found by setting up an equation based on their starting points and the rates at which they are working.
Let's denote the time in hours it will take for them to candy the same number of apples as 't'. Justin starts with 15 apples and candies at a rate of 4 apples per hour, so after 't' hours, he will have 15 + 4t apples. Jayme starts with 10 apples and candies at a rate of 5 apples per hour, so after 't' hours, she will have 10 + 5t apples.
To find the time when they have the same number of candied apples:
15 + 4t = 10 + 5t
Solving for t, we get:
15 + 4t - 4t = 10 + 5t - 4t
15 = 10 + t
t = 15 - 10
t = 5 hours
So, it will take 5 hours for both Justin and Jayme to have the same number of candied apples. To find the total number of candied apples they will have together, we calculate:
Justin's apples after 5 hours: 15 + 4(5) = 15 + 20 = 35 apples
Jayme's apples after 5 hours: 10 + 5(5) = 10 + 25 = 35 apples
The total number of candied apples they will have is 35 apples each, so together they will have 35 + 35 = 70 candied apples.