In a biology course, students spend a total of 290 minutes in lab and lecture each week. The lab time is 70 minutes shorter than the lecture time. How many minutes do the students spend in lecture and how many minutes do students spend in lab per week?
The Correct Answer and Explanation is:
Let’s define the unknowns:
- Let L be the time spent in lecture.
- Let Lab be the time spent in lab.
We are given two pieces of information:
- The total time spent in both lab and lecture is 290 minutes per week.
So, the equation will be: L+Lab=290L + \text{Lab} = 290L+Lab=290 - The lab time is 70 minutes shorter than the lecture time, meaning: Lab=L−70\text{Lab} = L – 70Lab=L−70
Now, substitute the second equation into the first one:L+(L−70)=290L + (L – 70) = 290L+(L−70)=290
Simplify the equation:2L−70=2902L – 70 = 2902L−70=290
Add 70 to both sides:2L=3602L = 3602L=360
Now divide both sides by 2:L=180L = 180L=180
So, students spend 180 minutes in lecture.
Next, we substitute this value into the equation for lab time:Lab=180−70=110\text{Lab} = 180 – 70 = 110Lab=180−70=110
Therefore, students spend 110 minutes in lab.
Final Answer:
- Lecture time: 180 minutes
- Lab time: 110 minutes
Explanation:
This problem involves setting up two equations based on the given information and solving for the unknowns. The first equation represents the total time spent in both lab and lecture. The second equation represents the relationship between the lab and lecture times. By substituting one equation into the other, we can solve for the lecture time and subsequently find the lab time. This approach ensures that we account for the total time constraint and the difference between the lecture and lab times.
