PSHS NCE Rates, Work, and Distance Problems Reviewer

TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Rates, Work, and Distance Problems

Use the right relationship quickly: distance = rate × time, unit rate, and simple work-rate thinking.

Grade 6–7 friendlyRate × TimeRegular practiceQuick Fire + Mastery

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Rates, Work, and Distance Problems

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Rate tells how much happens in one unit of time

A cyclist travels 60 km in 3 hours.

60 ÷ 3 = 20 km/h

The rate is 20 km per hour.

Three useful relationships:
Distance = Rate × Time
Rate = Distance ÷ Time
Time = Distance ÷ Rate

DO IT FAST

Use WHAT DO I NEED?

1. Need distance? Multiply rate × time.
2. Need rate? Divide distance ÷ time.
3. Need time? Divide distance ÷ rate.
4. Need work per hour? Think “fraction of the job completed in one hour.”

Fast clue: If the problem gives “per hour,” “per minute,” or “each,” you are probably dealing with a rate.

WORKED EXAMPLES

Six patterns you should recognize

1. Find distance

A car travels at 50 km/h for 4 hours.

50 × 4 = 200 km

200 km

2. Find rate

A runner covers 18 km in 3 hours.

18 ÷ 3 = 6 km/h

6 km/h

3. Find time

A bus travels 180 km at 60 km/h.

180 ÷ 60 = 3 hours

3 hours

4. Unit rate

5 notebooks cost ₱150.

₱150 ÷ 5 = ₱30 each

₱30 per notebook

5. Simple work rate

A machine can finish a job in 4 hours.

In one hour it finishes 1/4 of the job.

Work rate = 1/4 job per hour

6. Combined work

Machine A does 1/4 of a job per hour. Machine B does 1/4 per hour.

1/4 + 1/4 = 1/2 job per hour

Together they finish in 2 hours.

TRY WITH ME

Pick the missing quantity

A van travels 240 km at 60 km/h. How long does the trip take?

1. We know distance and rate.
2. We need time.
3. Time = distance ÷ rate.
4. 240 ÷ 60 = 4.

4 hours

COMMON TRAPS

Watch out for these

Multiplying when you should divide.
Ask first: am I looking for distance, rate, or time?

Ignoring units.
Hours and minutes must match.

Treating work time like ordinary addition.
If one worker takes 4 hours, the rate is 1/4 job per hour.

Missing “each” or “per.”
Those words usually signal unit rate.

REGULAR PRACTICE

Build the skill

These mix distance-rate-time, unit rates, and simple work-rate questions.

QUICK FIRE

Can you choose the right operation fast?

Five short questions. Decide whether to multiply or divide before calculating.

Question 1 of 5

FRESH MASTERY CHECK

Can you do it without hints?

Score 5/5 to verify this competency. If you miss one, a fresh set will be ready.

NEED HELP?

Rate problems still slowing you down?

Send Teacher Abi the problem that confused you and your result. I can help you identify what the problem is really asking for.

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