You wish to download a file from the internet. Your internet download speed is 890 kilobytes per second. How many minutes would it take you to download a 350 megabyte file?

(1 megabyte = 1,000 kilobytes)

Summary Submit Skip Question

If you have trouble figuring out where to start, try to list all the given quantities and conversion factors as fractions. Don't worry if you're missing some or if they are in the right order.

For unit conversion problems, we need to arrange the fractions so that when multiplied, the units cancel out until we obtain the one that we want. We can flip any of our fractions (since conversion factors are really just \(\frac{1}{1}\)).
Starting with our given, and arranging the conversion factors accordingly,

$$\small \frac{350 \text{ megabytes}}{1} $$ $$\small \frac{350 \cancel{\text{ megabytes}}}{1} \cdot \frac{1{,}000 \text{ kilobytes}}{1 \cancel{\text{ megabyte}}}$$ $$\small \frac{350 \cancel{\text{ megabytes}}}{1} \cdot \frac{1{,}000 \cancel{\text{ kilobytes}}}{1 \cancel{\text{ megabyte}}} \cdot \frac{1 \text{ second}}{890 \cancel{\text{ kilobytes}}} $$ We know we can stop when we obtain our desired unit. If we have no more conversions to use, it may mean you are missing one or two. $$ \small \frac{350 \cancel{\text{ megabytes}}}{1} \cdot \frac{1{,}000 \cancel{\text{ kilobytes}}}{1 \cancel{\text{ megabyte}}} \cdot \frac{1 \cancel{\text{ second}}}{890 \cancel{\text{ kilobytes}}} \cdot \frac{1 \textbf{ minute}} {60 \cancel{\text{ seconds}}} $$ A bit of work for the calculator: $$ \frac{350}{1} \cdot \frac{1{,}000}{1} \cdot \frac{1}{890} \cdot \frac{1}{60} \text{ minutes}$$ $$ \approx \boxed{6.55 \text{ minutes}} $$

Although a systematic approach is preferred, we can do these problems without a rigid structure. We can use the provided information to obtain that a 350 megabyte file would be 350,000 kilobytes. Since every 890 kilobytes takes one second, 350,000 kilobytes would take \(\dfrac{350{,}000}{890}\) seconds \( \approx 393\) seconds. Finally, we divide 393 by 60 since there are that many seconds in a minute to obtain our final answer, \( \approx 6.55\) minutes.

Although approach 2 seems way easier, approach 1 works for almost any unit conversion problem, especially the more difficult ones. Intuition and inspection can only get us so far for word problems we are unfamiliar with.