The Sun is approximately 1,400 million kilometers from the planet

The Sun is approximately $1{,}400$ million kilometers from the planet Saturn, and light from the Sun travels to Saturn at the rate of approximately $300{,}000$ kilometers per second. Approximately how many minutes does it take for light to travel from the Sun to Saturn?

  1. $80$
  2. $130$
  3. $160$
  4. $280$
  5. $360$

So, you were trying to be a good test taker and practice for the GRE with PowerPrep online. Buuuut then you had some questions about the quant section—specifically question 11 of the second Quantitative section of Practice Test 1. Those questions testing our knowledge of Ratios and Proportions can be kind of tricky, but never fear, PrepScholar has got your back!

Survey the Question

Let’s search the problem for clues as to what it will be testing, as this will help shift our minds to think about what type of math knowledge we’ll use to solve this question. Pay attention to any words that sound math-specific and anything special about what the numbers look like, and mark them on your paper.

This question gives us a sentence with distance, speed, and time. We know that for any particular speed, the ratio between the distance traveled and the time traveled is constant. We should expect to use our math skills related to Ratios and Proportions.

What Do We Know?

Let’s carefully read through the question and make a list of the things that we know.

 

  1. The distance between the Sun and Saturn is $1{,}400$ million kilometers
  2. Light travels from the Sun to Saturn at a speed of $300{,}000$ kilometers per second
  3. We want to calculate the time in minutes it takes for light to travel from the Sun to Saturn

 

Develop a Plan

We know the relationship between distance, speed, and time is:

$$\Time = \Distance / {\Speed}$$

We do need to be careful with the units though. The distance is given in millions of kilometers, but the speed only has kilometers in it. We also want the time in minutes, but the speed has seconds in it. So we’ll need to check the units closely as we solve this problem.

Solve the Question

Using our equation to solve for Time, we get:

$\Time$ $=$ ${\Distance}/{\Speed}$
$ $ $ $ $ $
$\Time $ $=$ $({1{,}400}/{300{,}000})·({\million \kilometers·\seconds}/{\kilometers}) $

Alright, so we’re making good progress here. We notice that we still have “million kilometers” and “kilometers” in the units. That looks kind of awkward. Let’s figure out a way to simplify them more.

We know that for unit conversions, we can multiply by any conversion if the top and bottom of the fraction are equal. So we need to find an equation relating “million kilometers” and “kilometers” to get them to cancel:

$$1 \million \kilometers = 1{,}000{,}000 \kilometers$$

Excellent. Let’s use this conversion, remembering to put the units we want to cancel on the opposite side of the fraction than where they previously were. Since “million kilometers” is on the top, we need it on the bottom so that it cancels. Multiplying our previous answer with this conversion, we get:

$\Time $ $=$ $({1{,}400}/{300{,}000})·({\million \kilometers·\seconds}/{\kilometers}) ·({1{,}000{,}000 \kilometers}/{1 \million \kilometers})$
$ $ $ $ $ $
$\Time$ $=$ $({1{,}400{,}000{,}000}/{300{,}000}) \seconds$

Goodness that’s a lot of $0\s$! Let’s first cancel out some $0\s$ from the numerator and denominator. We see that the denominator has five $0\s$, so let’s cancel out five $0\s$ from the numerator and denominator.

$$\Time = ({14{,}000}/3)\seconds$$

The question asks us for time measured in minutes. Since we know the conversion between minutes and seconds, let’s multiply our answer by that conversion to get the number of minutes. We can see that “seconds” is on the top right now, so we know that our conversion should have “seconds” on the bottom for it to cancel out.

$\Time$ $=$ $({14{,}000}/3) \seconds · ({1 \minute}/{60 \seconds})$
$\Time$ $=$ ${14{,}000}/{3·60} \minutes$
$\Time$ $=$ $77.78 \minutes$

Great! Checking the answer choices, $80$ minutes is the closest to our answer. The correct answer is A, $80$.

What Did We Learn

Definitely need to be careful with unit conversions. Writing everything out and taking our time counting the $0\s$ that we needed to cancel definitely helped a lot here.

 

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