# Rates & Distances

Distance, rate and time problems are commonly tested on the GRE. These problems are a common type of algebra problem encountered on the test, which test setting up equations and working with variables.

## Rule

Distance equals rate multiplied by time.

If there are different rates for different periods of time, distance equals each rate multiplied by each unit of time.

For example, if a ship is traveling at 20 nautical miles per hour for 1.1 hours, the ship will travel a total of 22 nautical miles.

## Practice

1. A train travels 360 miles over the course of 8 hours. How fast does the train travel?

2. A car travels at 45 miles per hour. How long will it take for the car to travel 225 miles?

3. If a truck travels 175 miles over the course of 3.5 hours, how fast is the truck traveling?

A common problem on the GRE is the so-called "brain-lapse mistake", where the person knows how to solve the problem but merely "spaces" mentally and puts the wrong number in the wrong part of the equation.

Rate and time problems, along with problems involving ratios and percentages are a common source of brian-lapse mistakes and thus test-takers who struggle with this particular problem should make sure to double-check rate and time problems on their GRE.

1. 45 miles per hour

Distance equals rate multiplied by time, thus:

360 = r(8)

Take our initial equation.

45 = r

Divide both sides by 8.

2. 5 hours

Distance equals rate multiplied by time; thus

t(45) = 225

Take the initial equation.

t = 5

Divide both sides by 45.

3. 50 miles per hour

Distance equals rate multiplied by time, thus:

r(3.5) = 175

Take the initial equation.

r = 50

Divide both sides by 3.5.