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Question 843510: An engineer undertakes a project to build a road of 15 km long in 300 days and employs 45 men for the purpose.after 100 days he finds only 2.5 km of the road has been completed.find the number of extra men he must employ to finish the work in time.with process.
Found 2 solutions by richwmiller, Theo:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 45*100=4500 man days for 2.5 km
The road will take 15/2.5=6 times 100=600 total days to finish or 500 more days
There is already 2.5 finished so for 12.5 km 12.5/2.5=5
so he needs 4500*5 man days. 22500 man days/200 =112.5 men to finish the job in 200 more days.
We can't just hire a half a man so we will need 113 men total 113-45=68 more men.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! The basic formula to use is RT = Q
R is the overall combined rate of work.
T is the time required to do the work.
Q is the quantity of work that has to be done.
In this problem, the original job was for 45 men to complete 15 kilometers of road in 300 days.
What actually happened is that 45 men completed only 2.5 kilometers of the road in 100 days.
The actual rate that the 45 men performed at would be based on the following formula.
Rate * Time = Quantity of work performed.
R = Rate in kilometers of road constructed per day.
T = Time in days.
Q = Kilometers of road completed.
This formula is shown as RT = Q.
RT = Q becomes:
R * 100 = 2.5
Solve for R to get R = 2.5 / 100 = .025 kilometers of road per day.
The 45 men are working at a combined rate of .025 kilometers of road per day.
Multiply that by 100 and you get 45 men completed 2.5 kilometers of road in 100 days.
This is the combined rate that the 45 men are currently working at.
What is left to do is the following:
The project has to complete an additional 12.5 kilometers of road in the remaining 200 days.
The formula for that will be:
RT = Q which becomes:
R * 200 = 12.5
Solve for R to get R = 12.5 / 200 = .0625 kilometers of road per day.
Since 45 men are working at a combined rate of .025 kilometers per day, and the engineer needs a combined rate of .0625 kilometers per day, the engineer will need more men who, working at the same rate as the original 45 men, will be able to attain a combined rate of .0625 kilometers per day.
A ratio is set up to determine how many additional men will be required.
The ratio is:
45 / .025 = x / .0625
This ratio says that 45 men are to .025 kilometers per day as x men are to .0625 kilometers per day.
Cross multiply to get 45 * .0625 = .025 * x
Divide both sides of the equation by .025 to get:
x = (45 * .0625) / .025 which makes x = 112.5
The engineer will require 112.5 men to complete the 12.5 kilometers of road in 200 days.
112.5 men, working at a combined rate of .0625 kilometers per day for 200 days will complete .0625 * 200 = 12.5 kilometers of road.
Since the engineer can't have a fraction of a man working on the project, the engineer will require 113 men.
This will allow the engineer to complete the project in just under 200 days,
Since the engineer already has 45 men, then the engineer requires 68 more men because 45 + 68 = 113 which is the total number of men required.
The answer you are looking for is 68 additional men need to be hired.
This will make a total of 113 men.
The combined rate of 113 men will be slightly higher than .0625 kilometers of road per day required. This means that the 113 men will complete the 12.5 kilometers of road in just under 200 days.
you can calculate the exact number of days required to complete 12.5 km of road using 113 men, but it's not required since 113 men is the smallest amount of whole men above 112.5 actually required that you will need. 112 men would not be able to complete the job in 200 days. They would take a little more than 200 days. 113 men will take a little less than 200 days. Go with 113 men.
The actual calculations would be as follows:
112.5 men work at a combined rate of .0625 kilometers per day.
This means that each man works at a rate of .0625 / 112.5 kilometers per man per day.
Multiply .0625 / 112.5 * 113 and you will get 113 men working at a combined rate of .0625 / 112.5 * 113 kilometers of road per day.
Divide 12.5 by (.0625 / 112.5 * 113) and you will get 199.1150442 days.
The 113 men will be working at a combined rate of .0627777777777 kilometers per day, as opposed to 112.5 men working at a combined rate of .0625 kilometers per day.
The exact number of days can be calculated, but it is not necessary, since 113 is the smallest whole number of 112.5 that can be required, so the total is 113 and the extra men required is 68.
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