Explore · MATH-5B-C14-L02-OPEN
A pump delivers 7 L/min. How many liters in 3 min?
Singapore Math 5B · Original independent course
Rate Problems — Part 1
Watch for: Multiplying when division is required for the unknown.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C14-L02-PREREQ
A cyclist goes 5 km/h for 2 hours. How far?
Show worked answer (after attempting)
Answer: 10 km
5 km/h × 2 h = 10 km.
Understand the idea
Solve single-rate quantity problems using equal scaling and dimensional reasoning. The essential earlier idea is: Chapter 14 rate definitions and prior multiplication/division of whole numbers.. The model below will always use the actual quantities from the worked problem. Check multiplying when division is required for the unknown when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C14-L02-Q01
A pump delivers 6 L/min. How many liters in 3 min?
Solution: 18 L
Rate × matching time = amount: 6 L/min × 3 time units = 18 L.
Worked example 2 · MATH-5B-C14-L02-Q02
A cyclist travels 7 km per hour for 4 hours. Find distance.
Solution: 28 km
Rate × matching time = amount: 7 km/h × 4 time units = 28 km.
Worked example 3 · MATH-5B-C14-L02-Q03
A printer makes 9 pages/min. How many pages in 5 minutes?
Solution: 45 pages
Rate × matching time = amount: 9 pages/min × 5 time units = 45 pages.
Check understanding
1 · MATH-5B-C14-L02-Q04
A pump delivers 7 L/min. How many liters in 3 min?
Show worked answer (after attempting)
Answer: 21 L
Rate × matching time = amount: 7 L/min × 3 time units = 21 L.
2 · MATH-5B-C14-L02-Q05
A cyclist travels 8 km per hour for 4 hours. Find distance.
Show worked answer (after attempting)
Answer: 32 km
Rate × matching time = amount: 8 km/h × 4 time units = 32 km.
3 · MATH-5B-C14-L02-Q06
A printer makes 10 pages/min. How many pages in 5 minutes?
Show worked answer (after attempting)
Answer: 50 pages
Rate × matching time = amount: 10 pages/min × 5 time units = 50 pages.
Guided practice
1 · MATH-5B-C14-L02-Q07
A pump delivers 8 L/min. How many liters in 3 min?
Show worked answer (after attempting)
Answer: 24 L
Rate × matching time = amount: 8 L/min × 3 time units = 24 L.
2 · MATH-5B-C14-L02-Q08
A cyclist travels 9 km per hour for 4 hours. Find distance.
Show worked answer (after attempting)
Answer: 36 km
Rate × matching time = amount: 9 km/h × 4 time units = 36 km.
3 · MATH-5B-C14-L02-Q09
A printer makes 11 pages/min. How many pages in 5 minutes?
Show worked answer (after attempting)
Answer: 55 pages
Rate × matching time = amount: 11 pages/min × 5 time units = 55 pages.
4 · MATH-5B-C14-L02-Q10
A pump delivers 9 L/min. How many liters in 3 min?
Show worked answer (after attempting)
Answer: 27 L
Rate × matching time = amount: 9 L/min × 3 time units = 27 L.
Independent practice
1 · MATH-5B-C14-L02-Q11
A cyclist travels 10 km per hour for 4 hours. Find distance.
Show worked answer (after attempting)
Answer: 40 km
Rate × matching time = amount: 10 km/h × 4 time units = 40 km.
2 · MATH-5B-C14-L02-Q12
A printer makes 12 pages/min. How many pages in 5 minutes?
Show worked answer (after attempting)
Answer: 60 pages
Rate × matching time = amount: 12 pages/min × 5 time units = 60 pages.
3 · MATH-5B-C14-L02-Q13
A pump delivers 10 L/min. How many liters in 3 min?
Show worked answer (after attempting)
Answer: 30 L
Rate × matching time = amount: 10 L/min × 3 time units = 30 L.
4 · MATH-5B-C14-L02-Q14
A cyclist travels 11 km per hour for 4 hours. Find distance.
Show worked answer (after attempting)
Answer: 44 km
Rate × matching time = amount: 11 km/h × 4 time units = 44 km.
5 · MATH-5B-C14-L02-Q15
A printer makes 13 pages/min. How many pages in 5 minutes?
Show worked answer (after attempting)
Answer: 65 pages
Rate × matching time = amount: 13 pages/min × 5 time units = 65 pages.
6 · MATH-5B-C14-L02-Q16
A pump delivers 11 L/min. How many liters in 3 min?
Show worked answer (after attempting)
Answer: 33 L
Rate × matching time = amount: 11 L/min × 3 time units = 33 L.
7 · MATH-5B-C14-L02-Q17
A cyclist travels 12 km per hour for 4 hours. Find distance.
Show worked answer (after attempting)
Answer: 48 km
Rate × matching time = amount: 12 km/h × 4 time units = 48 km.
8 · MATH-5B-C14-L02-Q18
A printer makes 14 pages/min. How many pages in 5 minutes?
Show worked answer (after attempting)
Answer: 70 pages
Rate × matching time = amount: 14 pages/min × 5 time units = 70 pages.
Challenge and error analysis
1 · MATH-5B-C14-L02-ERR1
The assigned question is: “A cyclist travels 15 km per hour for 4 hours. Find distance.” A learner wrote: “I divided the stated rate into the time instead of multiplying rate by time for 15, and found 60.1 km.” 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: 60 km
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 60 km. Recompute from the given data: Rate × matching time = amount: 15 km/h × 4 time units = 60 km.
2 · MATH-5B-C14-L02-ERR2
The assigned question is: “A printer makes 17 pages/min. How many pages in 5 minutes?” A learner wrote: “I divided the stated rate into the time instead of multiplying rate by time for 17, and found 86 pages.” 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: 85 pages
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 85 pages. Recompute from the given data: Rate × matching time = amount: 17 pages/min × 5 time units = 85 pages.
Exit check
Exit · MATH-5B-C14-L02-Q19
A pump delivers 12 L/min. How many liters in 3 min?
Show worked answer (after attempting)
Answer: 36 L
Rate × matching time = amount: 12 L/min × 3 time units = 36 L.