In the following question for example:

$1$ Neptune day = $18$ hours.

$1$ Earth day = $24$ hours.

How many Neptune days = $10$ Earth days?

My intial reaction was to do the following: $$\frac{18..Hours (on.Neptune)} {24..Hours (on.Earth)}=\frac{x..Neptune.Days} {10..Earth.Days}$$

Solving for $x$ gives $7.5$

By the answer is actually given by $$\frac{24..Hours (on.Earth)} {18..Hours (on.Neptune)}=\frac{x..Neptune.Days} {10..Earth.Days}$$

Solving for $x$ giving $12.33$

The confusing part is that on the Left, it is Earth/Neptune, but on the right, it it Neptune/Earth. This lead me to write the equation wrong intially as I would have thought it would be Neptune/Earth=Neptune/Earth.

$$\frac{24..Hours (on.Earth)} {18..Hours (on.Neptune)}=\frac{x..Neptune.Days} {10..Earth.Days}$$

Or in more simple terms:

$1$ Neptune day = $18$ hours.

$1$ Earth day = $24$ hours.

In $1$ Earth day ($24$ Hours), we have $24/18$ Neptune Days. In $10$ Earth days, we have $10*24/18=12.3 $ Neptune Days.

This way is quite clear and I wouldn't usually make a mistake in it. But I would like to be able to do it using the ratios to mechanise the process (as I need to do it in exam conditions where time is limited).

But I often end up getting the ratios the wrong way around.


Start with the thing you're given, then multiply by things that equal 1 until it's in the form you're trying to get to:

$$\begin{eqnarray}10 \text{ Earth days} & = & 10 \text{ Earth days} \times 1 \times 1 \\ & = & 10 \text{ Earth days} \times \frac{24 \text{ hours}}{1 \text{ Earth day}} \times \frac{1 \text{ Neptune day}}{18 \text{ hours}}\\ & = & \frac{10 \text{ Earth days}}{1 \text{ Earth day}} \times \frac{24 \text{ hours}}{18 \text{ hours}} \times 1 \text{ Neptune day}\\ & = & 12.33 \text{ Neptune days}\end{eqnarray}$$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.