2465.11 – The Luxury Yacht Gemini

Let $s$ be the ship's age; $b$ be the boiler's age; and $x$ be the number of years to subtract to get back to the time when "the ship was as old as the boiler is now." There are three equations. One gives the sum of the ages of ship and boiler:

$$\begin{equation}s + b = 49\end{equation}$$

Another is some years back, say $x$ years back, when "the ship was as old as the boiler is now:"

$$\begin{equation}s - x = b \leadsto s - b = x\end{equation}$$

Finally the Gemini is now twice as old as the boiler was back then:

$$\begin{equation}s = 2 (b - x) = 2b - 2x\end{equation}$$

Combining $(2)$ and $(3)$ we can get a second equation that, like $(1)$, only has $s$ and $x$ in it:

$$\begin{aligned}s &= 2b - 2x \\&= 2b - 2(s - b) \\&= 4b - 2s \\\leadsto 3s &= 4b.\end{aligned}$$

So let us next take (1) and multiply it by 3.

$$\begin{aligned}3s &= 3 (49 - b) \\&= 147 - 3 b \\\leadsto 4b &= 3s \\&= 147 - 3b \\\leadsto 7b &= 145 \\b &= 21.\end{aligned}$$

Knowing $b$, we find that $s$ = 49 - b = 28. Incidentally, $x = 7.$

By the way, there is (or was) a wonderful yacht named Gemini, that once belonged to the Duke of Windsor. Do Google images for "yacht Gemini 1941" and you can find a picture of it. Stella sailed on that yacht twice in 1969, the date in which this problem is set.