## Solving Rate Problems

### Algebra: Rates and Proportions Help

Rate problems are basically easy but you have to make sure you keep the units straight. That's because rate problems involve a lot of multiplying and dividing.

For example, if a guy travels 500 km in 20 hours, we find out his speed by dividing 500 km by 20 hours to get 25 km/hour. Notice that km/hour is a fraction that we get by dividing km by hours.

Likewise, if we know that his speed is 25 km/hour and he travels for 20 hours we find out how far he travels by multiplying 25 km/hour by 20 hours to get 500 km. This time we multiply km/hour by hour to end up with just km since we are multiplying a fraction and a whole number.

Lastly, if we know he travels 500 km and his speed is 25 km/hour, we get his time by dividing 500 km by 25 km/hour to get 20 hours. This time we divide km by km/hour to end up with hours. If this seems a little hazy, you might want to review dividing a fraction and a whole number.

Sometimes you have to convert the units to solve the problem. For example, suppose you are given the rate of 25 km per hour and are asked the rate per minute. Since an hour is 60 minutes we change hours into minutes:

25 km per hour
= 25 km per 60 minutes
= 5/12 km per minute 