If 10 men working 7 hours a day dig a trench 147 m long, ____ men working 8 hours a day will dig a trench 168 m long (of the same breadth and depth as the first in the same number of days) .

Question

Infinity Learn · Accepted Answer

Concept: 10 men working 8 hours a day will dig a trench 168 m long. Assume that one man can dig a trench at a rate of x meters per hour.
For the other group of guys as well, this rate will be the same.
Using the knowledge that 10 men digging a 147-meter trench for 7 hours each day, find the value of x.
Find the necessary number of men, working 8 hours per day, to dig a 168 m trench using this value of x.
Here, it is not stated in the inquiry how many days the initial group of 10 men needed to dig the 147-meter trench. Let's say that they dug it in a single day.
Thus, the second group of workers will similarly need to dig a 168-meter trench in a single day. Given that both groups finish their task in the same number of days,
Let's now assume that each man can dig a trench x meters long per hour in a day.
∴ In one hour, 10 guys can dig a trench 10x meters long.
∴ They will dig a trench that is 70 meters long in 10 x 7 hours. ———- (1) As is well known, a 147 m long trench was dug by 10 men working 7 hours per day.
147m = 70x (from (1) )
⇒x=

\frac{147}{70}

=2.1m
The output of each man's labor is thus: P = excavating a 2.1-meter-long trench each hour over the course of a day. ——————- (2)
The other group of men will produce the same amount of labor.
Let's now assume that 168 meters of trench must be dug in eight hours by x guys.
We are aware that one man can dig a trench 2.1 meters long in an hour.
A trench 2.1 meters long can be dug by one man in an hour.
They will dig a 16.8 meter long trench in 8 hours.
This number must match 168.
⇒16.8y=168⇒y=

\frac{168}{16.8}

=10 males
Therefore, 10 men are required to dig a trench 168m long in 8hours a day.
Hence, the answer is 8 hours.

If 10 men working 7 hours a day dig a trench 147 m long, ____ men working 8 hours a day will dig a trench 168 m long (of the same breadth and depth as the first in the same number of days) .

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