# Rate, Time and Distance Problem

What is the relationship between rate, time and distance? Say a car is traveling at 30 mph, how far will it go in 2 hours?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

The formula Distance = Rate x Time expresses one of the most frequently used relations in algebra.

Since an equation remains true as long as you divide through by the same non-zero element on each side, this formula can be written in different ways:

To find rate, divide through on both sides by time:

Rate = Distance / Time

Rate is distance (given in units such as miles, feet, kilometers, meters, etc.) divided by time (hours, minutes, seconds, etc.). Rate can always be written as a fraction that has distance units in the numerator and time units in the denominator, e.g., 25 miles/1 hour.

To find time, divide through on both sides by rate:

Time = Distance / Rate

When using this equation, it's important to keep the units straight. For instance, if the rate the problem gives is in miles per hour (mph), then the time needs to be in hours, and the distance in miles. If the time is given in minutes, you will need to divide by 60 to convert it to hours before you can use the equation to find the distance in miles. Always make your units match: if the time is given in fortnights and the distance in furlongs, then the rate should be given in furlongs per fortnight.

You can see why this is true if you look carefully at how the units are expressed.

Your question: Say a car is travelling at 30 mph and you want to figure out how far it will go in 2 hours. You can use the formula:

Rate x Time = Distance

30 miles / hour x 2 hours = 60 miles

Notice that the hours cancel, leaving only miles.

I hope this is helpful.

BEST OF LUCK AND TAKE CARE!

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