If 36 bighas of land can be irrigated in 16 days by a well-pump working 15 hours a day, how many days will it

Question

If 36 bighas of land can be irrigated in 16 days by a well-pump working 15 hours a day, how many days will it take to irrigate 42 bighas of land using the same pump if it works 10 hours a day?

Accepted Answer

We can apply the work-rate equality formula for a constant efficiency pump:

\frac{W _{1}}{D _{1} \times H _{1}} = \frac{W _{2}}{D _{2} \times H _{2}}

Where:

*

W_{1} = 36 bighas

,

D_{1} = 16 days

,

H_{1} = 15 hours/day

*

W_{2} = 42 bighas

,

D_{2} = unknown required days

,

H_{2} = 10 hours/day

Substituting the parameters into the equation:

\frac{36}{16 \times 15} = \frac{42}{D _{2} \times 10}

\frac{36}{240} = \frac{42}{10 D _{2}}

\frac{3}{20} = \frac{42}{10 D _{2}}

Cross-multiplying to evaluate

D_{2}

:

3 \times 10 D_{2} = 42 \times 20

30 D_{2} = 840

D_{2} = \frac{840}{30} = 28 days

If $36 bighas$ of land can be irrigated in $16 days$ by a well-pump working $15 hours$ a day, how many days will it take to irrigate $42 bighas$ of land using the same pump if it works $10 hours$ a day?

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