Video: Solving Word Problems Involving Rates

William drives 233 km in 6 hours. Giving your answer correct to two decimal places, at this rate, how long would it take him to drive 398 km?

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Video Transcript

William drives 233 kilometers in six hours. Giving your answer correct to two decimal places, at this rate, how long would it take him to drive 398 kilometers?

We are told in the question that William drives 233 kilometers in a time of six hours. We need to calculate how long it will take him to drive 398 kilometers. In order to do this, we’ll begin by calculating the unit rate. This is the distance he will travel in one hour or per hour. Six divided by six is equal to one, so we need to divide 233 kilometers by six.

This can be done using the short division bus stop method as shown. 233 divided by six is equal to 38.83 recurring. At his current rate, William would drive 38.83 recurring kilometers in one hour.

Our next step will be to work out what we multiply this number by to give us 398 kilometers. The easiest way to do this would be to divide 398 by 38.83 recurring on a calculator. This gives us 10.2489 and so on. Rounding this to two decimal places gives us 10.25. The deciding number is the eight. And if this is five or greater, we round up. We can, therefore, conclude it would take William 10.25 hours to drive 398 kilometers.

An alternative way to solve this problem would be to use our speed–distance–time formula. We recall that speed is equal to distance divided by time. Distance is equal to speed multiplied by time, and time is equal to distance divided by speed. We could, therefore, calculate the average speed by dividing 233 by six. As previously calculated, this is equal to 38.83 recurring.

For the purposes of this method though, we will keep the answer as 233 over six. To calculate the time taken to drive 398 kilometers, we can divide this distance by the average speed. Dividing 398 by 233 over six is the same as multiplying 398 by six over 233. This is equal to 10.2489 and so on, which once again rounds to 10.25 hours. It would take William 10.25 hours, to two decimal places, to drive 398 kilometers.

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