Question

it takes 8 soldiers 36 minutes to dig a hole 18 feet long by 10 feet wide. how long will it take 5 doliders to dig a hole 20 feet by 15 feet

Answer 1

Step-by-step explanation:

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Like many word problems, this one requires some assumptions.

All soldiers can dig at the same rate (i.e.: cubic feet of dirt per minute);

All 8 soldiers dug for the entire 36 minutes;

All 5 soldiers will dig for the entire time necessary to excavate the hole; and

The ground is uniformly diggable (i.e.: there are no more difficult / less difficult areas for digging).

For the 8 soldiers case, we have:

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Volume of hole is 4 feet x 18 feet x 10 feet = 720 cubic feet of dirt.

720 cubic feet of dirt / 8 soldiers = 90 cubic feet of dirt per soldier.

90 cubic feet of dirt per soldier / 36 minutes = 2.5 cubic feet of dirt per minute per soldier.

For the 5 soldiers case we have:

Volume of hole is 4 feet x 20 feet x 15 feet = 1200 cubic feet of dirt.

1200 cubic feet of dirt / 5 soldiers = 240 cubic feet of dirt must be dug by each soldier.

240 cubic feet of dirt per soldier / 2.5 cubic feet of dirt per minute per soldier = 96 minutes.

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With problems of this sort, keeping the units with the numbers is always helpful because it makes the resulting answer (and steps getting there) more understandable and it helps us to know whether we made a mistake along the way.