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Read the following prompt and answer the questions. Please make sure to number your responses to the questions as they are shown (1, 2, 3).

Prompt:

Jack can build 1/5 of a shed in the same time that Kyle can build 5/8 of a shed.

How much of a shed will Jack have built when Kyle has finished building 1 shed?



Describe one way you can explain this situation and make it easier to understand.

Explain how you would solve the problem. Include an answer to the problem with your explanation.

Read a post from another student. If you disagree with the answer or explanation in the post, explain why you disagree. If you agree with the answer and explanation, offer an extra reason why the answer is right.

1 answer

  1. To explain the situation more easily, we can compare the rates at which Jack and Kyle work. If we assume that both Jack and Kyle work at constant rates, we can establish a ratio or a common time frame to analyze their progress. Instead of considering fractions of sheds, we can think in terms of how long it takes each to complete a full shed, then see how much Jack accomplishes in that same time.

  2. To solve the problem, we first determine the time it takes Kyle to build 1 full shed. According to the prompt, Kyle can build 5/8 of a shed in the same time that Jack builds 1/5 of a shed. Let's denote the time it takes Jack to build 1/5 of a shed as T. Thus, in time T, Kyle builds 5/8 of a shed.

Now we need to find how much of a shed Jack can build in the time it takes Kyle to build 1 full shed. Since Kyle builds 5/8 of a shed in T, it would take him (1 / (5/8)) * T = (8/5) * T to build 1 full shed.

During the time Kyle is building 1 shed (which takes (8/5) * T), Jack will work for that same amount of time and can build:

  • In time T, Jack builds 1/5 of a shed.
  • In (8/5) * T, Jack will build (8/5) * (1/5) = 8/25 of a shed.

Therefore, when Kyle finishes building 1 shed, Jack will have built 8/25 of a shed.

  1. If I were to read a post from another student who proposed that Jack would build a different fraction, I would explain that their misunderstanding might stem from the incorrect interpretation of the time relationship between Jack and Kyle. Since we calculated the time it takes Kyle to complete a shed based on the amount Jack can build in the same time, it directly affects the total work done by Jack. If they arrived at a different fraction such as 1/5 of a shed instead of the correct 8/25, I would clarify the calculations and emphasize the importance of using the same time frame for both individuals to determine their respective shed completion rates. If they agree on the answer, I would add that understanding the ratios and time correspondence is crucial in similar work-rate problems, which can be applied to various contexts.