Answer:
1.5 hours= 1hr 30m
Step-by-step explanation:
90÷15=6
6÷2=3
48÷16=3
3÷2=1.5
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Using proportional variables, it is found that it will take 1.5 hours for 16 men to dig a trench 48 m long.
The time needed is direct proportional to the length of the trench, and inverse proportional to the number of men, thus, the equation is:
[tex]t = k\frac{l}{m}[/tex]
In which:
15 men can dig a trench of 90 m long in 3 hours, thus [tex]m = 15, l = 90, t = 3[/tex], this is used to find k.
[tex]t = k\frac{l}{m}[/tex]
[tex]3 = k\frac{90}{15}[/tex]
[tex]6k = 3[/tex]
[tex]k = \frac{3}{6}[/tex]
[tex]k = 0.5[/tex]
Thus:
[tex]t = 0.5\frac{l}{m}[/tex]
16 men, 48m long, thus [tex]l = 48, m = 16[/tex], and the time is:
[tex]t = 0.5\frac{l}{m} = 0.5 \times \frac{48}{16} = 0.5(3) = 1.5[/tex]
It will take 1.5 hours for 16 men to dig a trench 48 m long.
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