1Cademy - Example: Finding Travel Time for Thanh and Nhat Moving in Opposite Directions

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Solving a Uniform Motion Application: Finding Travel Time for Trucks Moving in Opposite Directions

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Example: Finding Travel Time for Thanh and Nhat Moving in Opposite Directions

Apply the distance, rate, and time problem-solving strategy to find the unknown travel time when two people depart from the same point and move in opposite directions.

Problem: Thanh and Nhat leave their office in Sacramento at the same time. Thanh drives north on I-5 at a speed of $72$ miles per hour. Nhat drives south on I-5 at a speed of $76$ miles per hour. How long will it take them to be $330$ miles apart?

Read and draw: Sketch the scenario with an arrow pointing north ( $72$ mph) and another pointing south ( $76$ mph), leaving from a shared starting point. The total separation distance is $330$ miles. Create a rate–time–distance table.
Identify: The travel time until they are $330$ miles apart.
Name: Let $t$ = the travel time in hours. Multiply each rate by $t$ to determine the individual distance expressions:

	Rate (mph)	Time (hrs)	Distance (miles)
Thanh	$72$	$t$	$72t$
Nhat	$76$	$t$	$76t$
			$330$

Translate: Because they are traveling in opposite directions from the same origin, the total distance is the sum of the two individual distances: $72t + 76t = 330$
Solve: Combine like terms: $148t = 330$ . Divide both sides by $148$ : $t = \frac{165}{74}$ .
Check: Thanh's distance: $72 \cdot \frac{165}{74} = \frac{5{,}940}{37}$ miles. Nhat's distance: $76 \cdot \frac{165}{74} = \frac{6{,}270}{37}$ miles. Total distance: $\frac{5{,}940}{37} + \frac{6{,}270}{37} = \frac{12{,}210}{37} = 330$ miles. $\checkmark$
Answer: It will take them $\frac{165}{74}$ hours (approximately $2.23$ hours) to be $330$ miles apart.

Updated 2026-05-25

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OpenStax Intermediate Algebra

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