Topic

Distance and time related questions in linear equations

My Progress

Pug Score

0%

Best Streak

0 in a row

Study Points

+0

Unlock Full Access
Adaptive practice
Video lessons

Read

Distance-Time Word Problems

A distance-time word problem uses distance equals rate times time to model travel, such as two vehicles moving toward each other. Name the time as the unknown, write each distance as rate times time, and combine them into one linear equation. See a worked two-car example solved step by step.

Setting up a distance-time word problem

A distance-time word problem uses the relationship distance = rate × time to model travel. When two objects move toward each other, or one chases another, you can add or compare their distance expressions to build a linear equation.

Two cars start 300 miles apart and drive toward each other, one at 50 mph and the other at 70 mph. Let t be the time in hours until they meet. Each car's distance traveled is its rate times t, and together their distances must add up to 300 miles.

Setting up a distance-time word problem Two cars start 300 miles apart and drive toward each other, one at 50 miles per hour and the other at 70 miles per hour. Using distance equals rate times time for each car, the equation 50t plus 70t equals 300 gives 120t equals 300, so t equals 2.5 hours. 50 mph 70 mph 300 miles apart Setting up the equation Let t = time (hours) until they meet. distance = rate × time, for both cars combined: 50t + 70t = 300 120t = 300 → t = 2.5 hours
Each car's distance is rate × time; the two distances together cover the 300 miles.

The equation is 50t + 70t = 300, which simplifies to 120t = 300, so t = 2.5 hours.

The same rate × time modeling works whether objects move toward each other, apart, or one catches up to another — only the relationship between the distances changes. It follows the same naming-then-equation process as money word problems, unknown-number word problems, and rectangle word problems.

Related lessons