Math Homework. Do It Faster, Learn It Better.

Rate-Time-Distance Problems

When you have a rate of motion, such as x feet per y seconds, or x miles per y hours, you can use the important relationship

rate × time = distance

to solve many problems.

Example 1:

If you ride your cycle at a speed of 15 miles an hour in a straight line, how far will you be from your starting place after 3 hours?

The rate is 15 miles 1 hour , and the time is 3 hours.


15 miles 1 hour 3 hours = 45 miles

So, you will be 45 miles from your starting place.

Example 2:

Light leaving the Sun takes about 8 minutes to reach the Earth, traveling a distance of approximately 93,000,000 miles. Find the speed of light in miles per second.

The rate is unknown. The time is 8 minutes and the distance is 93,000,000 miles.

Set up an equation.

r 8 minutes = 93,000,000 miles

Divide both sides by 8 minutes.

r = 93000000 miles 8 minutes

Divide 93,000,000 by 8 to reduce the fraction.

r = 11625000 miles minute

Divide by 60 to get miles per second.

r 193 , 750 miles second

So the speed of light is about 190 , 000 miles per second.