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Rates and speed
I worked these out from the practice questions. Each code says where to start reading, where to stop, what you can skip, and why it is safe.
1. Say the rate in words
- Start:
- Read the numbers and say them with per.
- Stop:
- Stop once you can say: ___ per ___.
- Skip:
- Skip the story around the numbers.
- Why:
- Questions 1, 2 and 3 are all one division, and saying per tells you which number goes first.
Used in questions 1, 2, 3
2. The time unit trap
- Start:
- Look at the unit in the last sentence.
- Stop:
- Stop when you see minutes or hours.
- Skip:
- Skip changing units before you know which unit is asked.
- Why:
- Question 4 gives 0.7 hour as a tempting answer, but the question asks for 42 minutes.
Used in question 4
3. Total over total
- Start:
- Find the total distance and the total time.
- Stop:
- Stop after dividing once.
- Skip:
- Skip averaging the two speeds.
- Why:
- Question 5 shows that 60 is wrong and 160 ÷ 3 is right.
Used in question 5
4. Together means add the rates
- Start:
- Write each rate as a part per hour.
- Stop:
- Stop when you have added the parts per hour.
- Skip:
- Skip adding or averaging the times.
- Why:
- In Question 6 the answer must be less than 3 hours, which removes 4.5, 3 and 9 at once.
Used in question 6
5. Difference or total
- Start:
- Read the last sentence for the words how much more.
- Stop:
- Stop when you know that you need to subtract.
- Skip:
- Skip the final multiplication until you subtract.
- Why:
- Question 7 offers both totals (60,000 and 75,000) as wrong options.
Used in question 7
6. Head start means closing speed
- Start:
- Find the gap when the second person starts.
- Stop:
- Stop when you divide the gap by the difference of the speeds.
- Skip:
- Skip dividing the gap by only one speed.
- Why:
- Question 8 gives 9:00 if you use Jean's speed only.
Used in question 8
7. Sense check with the options
- Start:
- Estimate before calculating.
- Stop:
- Stop when you know the answer should be bigger or smaller.
- Skip:
- Skip options that fail the estimate.
- Why:
- Questions 1, 6 and 8: a bus rate near 60, two taps faster than 3 hours, and a catch-up soon after 8:30.
Used in questions 1, 6, 8
8. Graph and table: read the end points, then divide
- Start:
- Find the distance and the time at the end of the graph or the last row of the table.
- Stop:
- Stop after you divide total distance by total time.
- Skip:
- Skip the speeds of the middle segments; they only matter for a question about that segment.
- Why:
- Question 13 asks for the average over all 4 hours, so the rest hour counts. Question 9 only needs one row.
Used in questions 9, 13, 14
9. Minutes and seconds are not decimals
- Start:
- Change time written as 1:12 or 6:15 into minutes by dividing the seconds or minutes part by 60.
- Stop:
- Stop when the time is in hours with a decimal you trust.
- Skip:
- Skip typing 1.12 or 6.15; it is a different number.
- Why:
- Question 11 (1 h 12 min = 1.2 h) and Question 14 (6:15 = 6.25 min) both fail if you write the clock time as a decimal.
Used in questions 11, 14
10. Net rate and meeting time
- Start:
- Decide whether the two rates help each other (add) or work against each other (subtract).
- Stop:
- Stop when you have one combined rate, then divide the gap or the amount by it.
- Skip:
- Skip dividing by a single speed.
- Why:
- Question 12 uses 25 − 10 = 15; Question 15 uses 18 + 12 = 30 after the head start; Question 16 uses total time including the rest.
Used in questions 12, 15, 16