Kieron has 13 workers he can use for a job - Edexcel - GCSE Maths - Question 12 - 2022 - Paper 2
Question 12
Kieron has 13 workers he can use for a job.
He knows that 6 workers would take 1 4/5 days to complete this job.
Show that Kieron has enough workers to finish this ... show full transcript
Worked Solution & Example Answer:Kieron has 13 workers he can use for a job - Edexcel - GCSE Maths - Question 12 - 2022 - Paper 2
Step 1
Find the total amount of work done by 6 workers in days
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
If 6 workers take 1 4/5 days to finish the job, we can convert this mixed number to an improper fraction:
1 4/5 = \frac{9}{5} \
Now, the total work done can be calculated as:
Total Work = Number of Workers × Time = 6 × \frac{9}{5} \text{ worker-days}
Step 2
Calculate the total work done in worker-days
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
This gives us:
Total Work = 6 × \frac{9}{5} = \frac{54}{5} \text{ worker-days}
Step 3
Determine the amount of work each worker can do
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Now, we need to find out how many days it would take 13 workers to complete this amount of work:
Let T be the time in days needed by 13 workers. Then,
Total Work = Number of Workers × Time = 13 × T
\frac{54}{5} = 13 × T
T = \frac{54}{5} \div 13 = \frac{54}{65} \text{ days}
Step 4
Show that Kieron can finish the job in less than 7 days
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Calculating the value of T gives:
T = \frac{54}{65} \approx 0.83 \text{ days}
Since 0.83 days is significantly less than 7 days, we can conclude that Kieron indeed has enough workers to finish this job in less than 7 days.
