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Sandra takes 28 hours to finish a rectangular tapestry. If she works at the

same rate, how long will it take her to finish a bigger rectangular tapestry
that is 50% longer and 30% wider? Give your answer correct to the
nearest hour.

User Edd Turtle
by
8.0k points

1 Answer

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Let's start by finding the area of the original tapestry. We know that:

Area = length x width

We don't know the exact dimensions, but we can assume that the length and width are equal, so we can call them both "x". Then:

Area = x * x = x^2

We're told that Sandra takes 28 hours to finish this tapestry, so her rate of work is:

Rate = Area / Time = x^2 / 28

Now we need to find the area of the larger tapestry. We're told that it's 50% longer and 30% wider than the original. If the original length and width were both x, then the new length is 1.5x (50% longer) and the new width is 1.3x (30% wider). So the area of the new tapestry is:

New area = (1.5x) * (1.3x) = 1.95x^2

Now we can use the same rate of work to find out how long it will take Sandra to finish the new tapestry:

New time = New area / Rate = (1.95x^2) / (x^2 / 28) = 54.6 hours

Rounding to the nearest hour, it will take Sandra approximately 55 hours to finish the bigger rectangular tapestry.

User Kramb
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