\frac{6}{5} is 1.2, which comes from "20% faster in soft soil".

\frac{5}{3}*\frac{6}{5} is the same as

\frac{5}{3}*1.2abhi758 wrote:

Working at their normal rates, 20 diggers can dig a 100-meter long trench in hard soil in 3 days. A construction company ordered the diggers to dig a 180-meter long trench in soft soil. If diggers can work 20% faster in soft soil than in hard soil, how many diggers are required to complete this task in 3 days?

25

28

29

30

32

It follows from the stem that in 3 days one digger can dig 5 meters of trench in hard soil. Therefore, his digging speed on hard soil is \frac{5}{3} meters per day. On soft soil his speed would be \frac{5}{3}*\frac{6}{5}= \frac{6}{3} meters per day or 6 meters in 3 days. If one digger can dig 6 meters of a trench in 3 days then we need \frac{180}{3} = 30 diggers to dig the entire 180-meter long trench in 3 days.

Here how do we arrive at the fraction \frac{6}{5}?

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