Jen was making cake pops for the bake sale. After 3 hours, she had completed half of the work. She called Maryna for help and together they finished everything in half an hour. How long would it take Maryna to finish the job alone if she replaced Jen after Jen baked for 3 hours?
"After 3 hours, she had completed half of the work"
... so it would take Jen 6 hours to do the entire job
"together they finished everything in half an hour"
... Jen does an additional [1/2 / 6] or 1/12 of the entire job
... so Maryna does 5/12 of the whole job in 1/2 hr
(5/12) / (1/2) = (6/12) / t ... the time for Maryna to finish on her own
... she would be doing 6/12 (half) of the whole job
t = (1/2 * 6/12) / (5/12) ... hrs
36 minutes
Let's break down the information given:
1. Jen completed half of the work in 3 hours.
2. Jen and Maryna finished the entire job together in half an hour.
To find out how long it would take Maryna to finish the job alone if she replaced Jen after 3 hours, we need to first determine how much work Jen can complete in 1 hour.
Since Jen completed half of the work in 3 hours, we can calculate her work rate as follows:
1 hour of work / 3 hours = 1/3 of the work per hour.
Now that we know how much work Jen can complete in 1 hour we can find Maryna's work rate:
Jen and Maryna finished the entire job together in half an hour, so they completed 1/2 of the work in half an hour.
Using the work rate for Jen, we can determine Maryna's work rate as follows:
1/2 of the work / 0.5 hours = 1 of the work per hour.
Since Maryna's work rate alone is 1 of the work per hour, it would take Maryna 1 hour to complete the job by herself if she replaced Jen after Jen baked for 3 hours.
To find out how long it would take Maryna to finish the job alone if she replaced Jen after 3 hours, we first need to determine how much work Jen can do in 1 hour.
From the information given, we know that Jen completed half of the work in 3 hours. Therefore, we can conclude that in 1 hour, Jen can complete 1/3 of the total work.
Since Jen and Maryna worked together for 0.5 hours (half an hour) to finish the remaining half of the work, we can set up an equation:
Jen's work rate * Jen's time + Maryna's work rate * Maryna's time = Remaining work
Substituting the values we have:
(1/3) * 3 + Maryna's work rate * 0.5 = 1/2
Simplifying the equation:
1 + 0.5 * Maryna's work rate = 1/2
0.5 * Maryna's work rate = 1/2 - 1
0.5 * Maryna's work rate = -1/2
Now we can solve for Maryna's work rate:
Maryna's work rate = (-1/2) / (0.5)
Maryna's work rate = -1
Since work rates cannot be negative, we can conclude from the equation that Maryna's work rate is 1.
Now that we know Maryna's work rate is 1, we can determine how long it would take her to finish the job alone. Since her work rate is 1, it means she can complete the whole job in 1 hour.
Therefore, it would take Maryna 1 hour to finish the job alone if she replaced Jen after Jen baked for 3 hours.