Question

A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

Answer 1

The relationship between men, work, and time can be written as: \[ \text{Men} \times \text{Work} \propto \text{Time} \] Assuming all other factors remain the same.

Given Data:

	Men	Tunnel Length	Days
Initial	140	1.5 km	60
Remaining	X	4.5 km	140

Step-by-Step Calculation:

We use the direct proportion formula: \[ X = 140 \times \frac{4.5}{1.5} \times \frac{60}{140} \]

Simplifying: \[ X = 140 \times 3 \times \frac{60}{140} = 3 \times 60 = 180 \]

Hence, the number of men required = \( \boxed{180} \)

Additional men needed: \[ 180 - 140 = \boxed{40} \]

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Final Answer:

40 additional men are required to complete the remaining 4.5 km tunnel in 140 days.

Answer 2

A contractor agreed to complete a road project in 200 days with 140 workers.

However, after 60 days, only \( \frac{1}{4} \) of the total road was completed.

The amount of work left: \[ 1 - \frac{1}{4} = \frac{3}{4} \]

Remaining time to complete the work: \[ 200 - 140 = 60 \text{ days} \]

Let \( x \) be the number of extra persons needed to complete the remaining \( \frac{3}{4} \) of the work in 60 days.

We use the work formula: \[ \frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2} \] where \( M \) = men, \( D \) = days, \( W \) = work

Substituting values: \[ \frac{140 \times 60}{\frac{1}{4}} = \frac{(140 + x) \times 60}{\frac{3}{4}} \]

Simplify both sides: \[ 4 \times 60 = \frac{(140 + x) \times 4}{3} \]

Multiply both sides by 3: \[ 240 \times 3 = (140 + x) \times 4 \Rightarrow 720 = 4(140 + x) \]

Solve for \( x \): \[ 140 + x = 180 \Rightarrow x = 180 - 140 = \boxed{40} \]

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Final Answer:

40 additional workers are needed to complete the remaining road on time.