Need help with proportionality and inverse proportionality

Question

7 workers can do the job in 20 days. After 4 days of work, there was a need to complete the work in 18 days (So they have 14 more days left). How many more workers need to be hired?

Can you please show how to solve step by step?

Thank You a lot!

Answer 1

7 workers do the job in 20 days

in 4 days they do 4/20 = 1/5 of the job. they need to complete 4/5 of the job in 14 days

they need to finish in 18 days, how many more workers do they need to speed up the work? rough guess would be 1 more worker, and turns out that's exactly what's needed

it takes 1 worker 7x20 = 140 days to do the job

to complete the job in 18 days, they need to do 4/5 the job in the next 14 days

it takes 1 worker 140 days to do the full job. it takes 1 worker 4/5x140 days to do 4/5 of the job

4/5 of 140 = 4(28)= 112 days

112/14 =16/2 = 8 workers needed. so add 1 more worker