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Algebra Level 1

Bill & Bob are building a new house for their dog, Lyca. Bill alone can finish building in 3 hours while Bob is more delicate and can complete the same task alone in 6 hours.

How many hours does it take for both of them to build Lyca's house?


The answer is 2.

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4 solutions

In 1 hour, Bill completes 1/3 of the whole work, and Bob completes 1/6 in an hour.

Thus, if they work together, they will complete 1/3+1/6 = 1/2 of the whole work in an hour.

So it will take 1/(1/2) = 2 hours to build Lyca's house.

Achille 'Gilles'
Nov 6, 2015

Ricky Ramcharitar
Jan 12, 2016

Recall:

Rate x Time = Distance

We can use this formula, but substitute Job for Distance:

Rate x Time = Job

Set Job = 1

Therefore the equation simplifies to:

Rate x Time = 1

Bill can do the job in 3 hours so the equation for Bill is:

R x 3 = 1

Solve for R

Bill's rate is: R = 1 3 R = \dfrac{1}{3}

Similarly, we can find Bob's rate like so:

R x 6 = 1

Solve for R

Bob's rate is: R = 1 6 R = \dfrac{1}{6}

Combine the both rates:

1 3 + 1 6 = 1 2 \dfrac{1}{3} + \dfrac{1}{6} = \dfrac{1}{2}

Their combined rate is: 1 2 \frac{1}{2}

Use Formula again:

R x T = 1

1 2 \dfrac{1}{2} x T = 1

T = 2

Bob Dilworth
Nov 6, 2015

Working at the same time, in 6 hours they would build 3 houses (Bill 2 and Bob 1) Therefore it will take 6/3 or 2 hours to build one.

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