Distance Rate Time Problems UPCAT Reviewer: Lesson and Practice

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Distance–Rate–Time Problems

Build one distance equation for each traveler, then connect the distances using the story.

5-10 minute lesson27 original questionsAdaptive practiceSaves progress

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Distance–Rate–Time Problems

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Build one distance equation, then connect the travelers

The core relationship is d=rt, but UPCAT-style questions usually hide which distance, rate, or time belongs in the equation.

distance = rate × timerate = distance ÷ timetime = distance ÷ rate

Convert units before calculating. For an entire trip, average speed is total distance ÷ total elapsed time, including stops. When travelers move toward each other, add their speeds. For catch-up in the same direction, subtract their speeds.

Draw the distance or gap

Mark starting points, direction, speed, and any delayed departure.

Use relative speed carefully

Towardopposite directions usually add; catching up in one direction uses a difference.

DO IT FAST

Decide what happens to the gap

Problem: Two vehicles are 180 km apart and move toward each other at 50 kmh and 40 kmh.

Recognize: Every hour, the first closes 50 km of the gap and the second closes 40 km. Together they close 90 km per hour.

time = 180(50+40) = 2 hours

For a same-direction catch-up, use the faster speed minus the slower speed because only that difference reduces the lead.

Why it works

Relative speed measures how quickly the distance between travelers changes. Adding or subtracting rates is justified by whether both motions reduce the gap or only one traveler gains on the other.

WORKED EXAMPLES

Five forms you should recognize

1. Basic distance

A van travels at 60 kmh for 2.5 hours.

d=rt=60(2.5)=150 km

2. Average speed with a stop

A trip covers 150 km in 2.5 hours of driving and includes a 30-minute stop. Total elapsed time is 3 hours:

average speed=1503=50 kmh

3. Meeting from opposite towns

Two vehicles 240 km apart approach at 50 kmh and 70 kmh.

closing speed=50+70=120 kmhtime=240120=2 hours

4. Catch-up after a head start

A slower vehicle has a 45-km lead at 60 kmh; a faster one follows at 75 kmh.

gain speed=75−60=15 kmhtime=4515=3 hours

5. Equal-distance round trip

A car travels 120 km at 60 kmh and returns 120 km at 40 kmh.

total distance=240 kmtotal time=12060+12040=2+3=5 haverage speed=2405=48 kmh

Do not simply average 60 and 40 because the car spends different amounts of time at the two speeds.

COMMON TRAPS

Check before you commit

• Mixing minutes with hours
• Averaging speeds instead of using total distance over total time
• Ignoring stopped time
• Adding speeds in a same-direction catch-up
• Subtracting speeds when travelers approach each other
• Finding meeting time but not the requested meeting location

FIVE-FORM SKILL CHECK

Do you need the lesson-or just practice?

One original question in each form recommends your next step. It does not yet verify mastery.

CHOOSE YOUR PRACTICE

Work at the level you need.

Foundations

Build the core procedure with immediate explanations.

Core Practice

Use mixed forms with less scaffolding.

UPCAT-Style Transfer

Apply the competency in unfamiliar representations.

FRESH MASTERY CHECK

Ready to verify this competency?

A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-form bank.

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Distance–Rate–Time Problems FAQ

Why are there two mastery sets?

An unsuccessful attempt loads a different five-question set so memorizing one set does not verify mastery.

Does 5/5 mean permanent mastery?

It verifies the competency today. Revisit it later through mixed practice and simulations.

RELATED COMPETENCIES

Continue your mathematics review.

Ratio and ProportionLinear EquationsWork-Rate Problems

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