Explore · MATH-5B-C14-L03-OPEN
A machine produces 13 parts/min. How many minutes for 39 parts?
Great Inheritance Mathematics Term B · Original independent course
Rate Problems — Part 2
Watch for: Combining mismatched units or assuming a constant rate without evidence.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C14-L03-PREREQ
A printer makes 6 pages/min. How many minutes for 24 pages?
Show worked answer (after attempting)
Answer: 4 min
24 pages ÷ 6 pages/min = 4 min.
Understand the idea
Solve reverse or multi-step rate problems that may require unit conversion. The essential earlier idea is: Rate part 1 and Chapter 9 conversions.. The model below will always use the actual quantities from the worked problem. Check combining mismatched units or assuming a constant rate without evidence when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C14-L03-Q01
A machine produces 12 parts/min. How many minutes for 36 parts?
Solution: 3.0 min
Time = quantity ÷ rate = 36 ÷ 12 = 3.0. Units cancel to time.
Worked example 2 · MATH-5B-C14-L03-Q02
A trip is 32 km at 8 km/h. Find hours.
Solution: 4.0 h
Time = quantity ÷ rate = 32 ÷ 8 = 4.0. Units cancel to time.
Worked example 3 · MATH-5B-C14-L03-Q03
At 15 L/min, how long is needed to transfer 30 L?
Solution: 2.0 min
Time = quantity ÷ rate = 30 ÷ 15 = 2.0. Units cancel to time.
Check understanding
1 · MATH-5B-C14-L03-Q04
A machine produces 13 parts/min. How many minutes for 39 parts?
Show worked answer (after attempting)
Answer: 3.0 min
Time = quantity ÷ rate = 39 ÷ 13 = 3.0. Units cancel to time.
2 · MATH-5B-C14-L03-Q05
A trip is 36 km at 9 km/h. Find hours.
Show worked answer (after attempting)
Answer: 4.0 h
Time = quantity ÷ rate = 36 ÷ 9 = 4.0. Units cancel to time.
3 · MATH-5B-C14-L03-Q06
At 16 L/min, how long is needed to transfer 32 L?
Show worked answer (after attempting)
Answer: 2.0 min
Time = quantity ÷ rate = 32 ÷ 16 = 2.0. Units cancel to time.
Guided practice
1 · MATH-5B-C14-L03-Q07
A machine produces 14 parts/min. How many minutes for 42 parts?
Show worked answer (after attempting)
Answer: 3.0 min
Time = quantity ÷ rate = 42 ÷ 14 = 3.0. Units cancel to time.
2 · MATH-5B-C14-L03-Q08
A trip is 40 km at 10 km/h. Find hours.
Show worked answer (after attempting)
Answer: 4.0 h
Time = quantity ÷ rate = 40 ÷ 10 = 4.0. Units cancel to time.
3 · MATH-5B-C14-L03-Q09
At 17 L/min, how long is needed to transfer 34 L?
Show worked answer (after attempting)
Answer: 2.0 min
Time = quantity ÷ rate = 34 ÷ 17 = 2.0. Units cancel to time.
4 · MATH-5B-C14-L03-Q10
A machine produces 15 parts/min. How many minutes for 45 parts?
Show worked answer (after attempting)
Answer: 3.0 min
Time = quantity ÷ rate = 45 ÷ 15 = 3.0. Units cancel to time.
Independent practice
1 · MATH-5B-C14-L03-Q11
A trip is 44 km at 11 km/h. Find hours.
Show worked answer (after attempting)
Answer: 4.0 h
Time = quantity ÷ rate = 44 ÷ 11 = 4.0. Units cancel to time.
2 · MATH-5B-C14-L03-Q12
At 18 L/min, how long is needed to transfer 36 L?
Show worked answer (after attempting)
Answer: 2.0 min
Time = quantity ÷ rate = 36 ÷ 18 = 2.0. Units cancel to time.
3 · MATH-5B-C14-L03-Q13
A machine produces 16 parts/min. How many minutes for 48 parts?
Show worked answer (after attempting)
Answer: 3.0 min
Time = quantity ÷ rate = 48 ÷ 16 = 3.0. Units cancel to time.
4 · MATH-5B-C14-L03-Q14
A trip is 48 km at 12 km/h. Find hours.
Show worked answer (after attempting)
Answer: 4.0 h
Time = quantity ÷ rate = 48 ÷ 12 = 4.0. Units cancel to time.
5 · MATH-5B-C14-L03-Q15
At 19 L/min, how long is needed to transfer 38 L?
Show worked answer (after attempting)
Answer: 2.0 min
Time = quantity ÷ rate = 38 ÷ 19 = 2.0. Units cancel to time.
6 · MATH-5B-C14-L03-Q16
A machine produces 17 parts/min. How many minutes for 51 parts?
Show worked answer (after attempting)
Answer: 3.0 min
Time = quantity ÷ rate = 51 ÷ 17 = 3.0. Units cancel to time.
7 · MATH-5B-C14-L03-Q17
A trip is 52 km at 13 km/h. Find hours.
Show worked answer (after attempting)
Answer: 4.0 h
Time = quantity ÷ rate = 52 ÷ 13 = 4.0. Units cancel to time.
8 · MATH-5B-C14-L03-Q18
At 20 L/min, how long is needed to transfer 40 L?
Show worked answer (after attempting)
Answer: 2.0 min
Time = quantity ÷ rate = 40 ÷ 20 = 2.0. Units cancel to time.
Challenge and error analysis
1 · MATH-5B-C14-L03-ERR1
The assigned question is: “A trip is 64 km at 16 km/h. Find hours.” A learner wrote: “64 ÷ 16 = 4.1. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 4.0 h
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 4.0 h. Recompute from the given data: Time = quantity ÷ rate = 64 ÷ 16 = 4.0. Units cancel to time.
2 · MATH-5B-C14-L03-ERR2
The assigned question is: “At 23 L/min, how long is needed to transfer 46 L?” A learner wrote: “46 ÷ 23 = 3. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 2.0 min
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 2.0 min. Recompute from the given data: Time = quantity ÷ rate = 46 ÷ 23 = 2.0. Units cancel to time.
Exit check
Exit · MATH-5B-C14-L03-Q19
A machine produces 18 parts/min. How many minutes for 54 parts?
Show worked answer (after attempting)
Answer: 3.0 min
Time = quantity ÷ rate = 54 ÷ 18 = 3.0. Units cancel to time.