Answer :
Sure! Let's solve each part of the question step by step.
### Question 1
Problem: How many days would it take 67 men to build a wall which 134 men can build in 3 weeks?
Solution:
- First, determine how many weeks 3 weeks are in days. Since 1 week is 7 days, 3 weeks equal [tex]\(3 \times 7 = 21\)[/tex] days.
- Now, use the concept of "man-days," which means the number of men multiplied by the number of days they work can be used to determine the total work done. So, for the 134 men working for 21 days:
[tex]\[
\text{Total man-days} = 134 \text{ men} \times 21 \text{ days} = 2814 \text{ man-days}
\][/tex]
- Next, find out how many days it would take for 67 men to complete the same amount of work:
[tex]\[
\text{Time for 67 men} = \frac{2814 \text{ man-days}}{67 \text{ men}} = 42 \text{ days}
\][/tex]
It would take 67 men 42 days to build the wall.
### Question 2
Problem: A car can complete a certain journey in 12 hours if it travels at 65 km/h. How much time will it take if it travels at 78 km/h?
Solution:
- First, calculate the total distance of the journey. Using the formula:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
For 65 km/h over 12 hours:
[tex]\[
\text{Distance} = 65 \text{ km/h} \times 12 \text{ hours} = 780 \text{ km}
\][/tex]
- Now, calculate the time it will take to travel the same distance at 78 km/h:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{780 \text{ km}}{78 \text{ km/h}} = 10 \text{ hours}
\][/tex]
Traveling at 78 km/h, it will take 10 hours to complete the journey.
I hope this helps! Let me know if you have any other questions.
### Question 1
Problem: How many days would it take 67 men to build a wall which 134 men can build in 3 weeks?
Solution:
- First, determine how many weeks 3 weeks are in days. Since 1 week is 7 days, 3 weeks equal [tex]\(3 \times 7 = 21\)[/tex] days.
- Now, use the concept of "man-days," which means the number of men multiplied by the number of days they work can be used to determine the total work done. So, for the 134 men working for 21 days:
[tex]\[
\text{Total man-days} = 134 \text{ men} \times 21 \text{ days} = 2814 \text{ man-days}
\][/tex]
- Next, find out how many days it would take for 67 men to complete the same amount of work:
[tex]\[
\text{Time for 67 men} = \frac{2814 \text{ man-days}}{67 \text{ men}} = 42 \text{ days}
\][/tex]
It would take 67 men 42 days to build the wall.
### Question 2
Problem: A car can complete a certain journey in 12 hours if it travels at 65 km/h. How much time will it take if it travels at 78 km/h?
Solution:
- First, calculate the total distance of the journey. Using the formula:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
For 65 km/h over 12 hours:
[tex]\[
\text{Distance} = 65 \text{ km/h} \times 12 \text{ hours} = 780 \text{ km}
\][/tex]
- Now, calculate the time it will take to travel the same distance at 78 km/h:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{780 \text{ km}}{78 \text{ km/h}} = 10 \text{ hours}
\][/tex]
Traveling at 78 km/h, it will take 10 hours to complete the journey.
I hope this helps! Let me know if you have any other questions.
