ASVAB & PiCAT Math Prep: Distance, Rate, and Time Vocabulary

Vocabulary and core mathematical principles for solving distance, rate, and time word problems on the ASVAB and PiCAT.

ASVAB

Armed Services Vocational Aptitude Battery; a standardized military exam featuring word problems involving distance, rate, and time.

PiCAT

An unproctored military assessment test taken prior to or alongside the ASVAB that tests math word problem concepts.

Distance Formula

The core formula describing the relationship between distance, rate, and time, expressed as $d = r \times t$.

Distance ($d$)

The total spatial measurement traveled by an object, determined by multiplying rate by time ($d = r \times t$).

Rate ($r$)

The speed at which an object moves, commonly expressed in units such as miles per hour.

Time ($t$)

The length or duration of travel, typically measured in hours or minutes in distance problems.

Combined Rate

The total speed at which two moving objects close or widen the distance between them, calculated as $r_1 + r_2$ when moving in opposite directions.

Against the Current Rate

The effective rate of a boat traveling upstream against a river current, represented algebraically as $r - c$, where $r$ is the boat speed in still water and $c$ is the current speed.

With the Current Rate

The effective rate of a boat traveling downstream pushed by a river current, represented algebraically as $r + c$, where $r$ is the boat speed in still water and $c$ is the current speed.

Speed in Still Water

The baseline speed of a boat ($r$) without any added or subtracted velocity from a water current ($c$).