MATH SOLVE

7 months ago

Q:
# 8. The mathematics workshop, made up of 15 exercises, is developed by 4 students in 3 hours. As a leveling process, the teacher leaves a workshop of 20 exercises on the same topic, for 2 students to solve. Is it possible for students to complete the workshop in 4 hours? Explain your answer. with markdown averaging

Accepted Solution

A:

For the 15-exercise workshop:
4 students complete it in 3 hours.
Let's calculate their rate per student:
Rate per student for the 15-exercise workshop = $$ \frac{15\:exe}{4stud\times3\:hr} $$
.
Now, calculate the rate per student:$$ \frac{15}{4\times3}=\frac{15}{12}=\frac{5}{4} $$ exercises per student per hour.
Now, let's use this rate to estimate the time needed for two students to complete the 20-exercise workshop:
For the 20-exercise workshop:
T be the time it takes for the two students to complete the 20-exercise workshop. We can set up the equation:
Total exercises=Rate per student× Number of students×Time
$$ 20=\frac{5}{4}\times2\times T $$
Now, solve for T:
$$ T=20\times\frac{4}{5\times2}=8 $$
So, it would take the two students 8 hours to complete the 20-exercise workshop.
Now, to determine if it's possible for students to complete the workshop in 4 hours, we compare the estimated time (8 hours) with the given time (4 hours).
Since 8 hours is longer than the given 4 hours, it is not possible for the two students to complete the workshop in 4 hours. They would need more time.