Jeff K. answered • 05/20/20

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Hi Tanya:

We need an equation, relating the sun's rotation tom Mercury's.

Let S = time it takes the sun to rotate once on its axis.

Let M = time it takes mercury to rotate once on its axis.

Then, the question tells us that: S = M / 2 - 3.92 . . . . . . . . . . (eqn 1)

Now, rearrange the equation to get M by itself.

Add 3,02 to both sides of eqn 1: S + 3.92 = M / 2

Multiply through by 2: 2(S + 3.92) = M

This gives an equation for M.

Plug in 25.38 for S (given): M = 2(25.38 + 3.92)

= 2(29.3)

= 58.6 days