Question

An astronomer is studying 4 constellations in the night sky. Constellation X is 5 times farther from Earth than Constellation W. Constellation Y is 1,000 times farther from Earth than Constellation X. Constellation Z is 100 times farther from Earth than Constellation Y. The astronomer discovers that Constellation Z is 3.3×1021 miles from Earth. How far is Constellation W from Earth?

Answer 1

6.6×10¹⁵ miles

Explanation:

You want the distance of W from Earth if X is 5 times that distance, Y is 1000 times the distance of X, and Z is 3.3×10²¹, which is 100 times the distance of Y.

Distance

Using W, X, Y, Z to represent the distances from Earth to the respective galaxies, we have ...

• X = 5W
• Y = 1000X = 5000W
• Z = 100Y = 500,000W

and ...

3.3×10²¹ = 0.5×10⁶×W

W = (3.3×10²¹)/(0.5×10⁶) = 6.6×10¹⁵ . . . . miles

Constellation W is 6.6×10¹⁵ miles from Earth.

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