Tutor MathsGuru: Ask me for your burning Maths questions!

[YLH88]

[quote]When both Machines P and Q are used, a book can be printed in 5 hours. When printing a book, Machine P broke down. As a result, it took 7 hours to complete the printing of the book. If it would take Machine Q 8 hours 20 minutes to print the book alone, (a) how long was Machine P used before it broke down? (b) how long would it take to print the book using only Machine P? [4 marks][Answer given: 2 hours before, 12½ h]



Q : 8 1/3 h --> 1 book
7 h --> 7 x 3/25 = 21/25 book
5 h --> 5 x 3/25 = 3/5 book

1 - 21/25 = 4/25 book

1 - 3/5 = 2/5 book

P : 2/5 book --> 5 h
4/25 book --> 4/25 x 5/2 x 5 = 2 h
1 book --> 5/2 x 5 = 12 1/2 h

a) It was 2 h.

b) It was 12 1/2 h[/quote]Hi all,

The above question is from Maha Bodhi 2010 P6 Prelim Paper 2 Qn 11, solution was posted in this link http://psle2010a.blogspot.com/2010/09/maha-bodhi-p6-prelim-2010-paper-2q11.html

but I don't understand the step 1 - 3/5 = 2/5 book, can someone please help ?? :?

Thank you.

[Tang]

YLH88:

[quote]When both Machines P and Q are used, a book can be printed in 5 hours. When printing a book, Machine P broke down. As a result, it took 7 hours to complete the printing of the book. If it would take Machine Q 8 hours 20 minutes to print the book alone, (a) how long was Machine P used before it broke down? (b) how long would it take to print the book using only Machine P? [4 marks][Answer given: 2 hours before, 12½ h]



Q : 8 1/3 h --> 1 book
7 h --> 7 x 3/25 = 21/25 book
5 h --> 5 x 3/25 = 3/5 book

1 - 21/25 = 4/25 book

1 - 3/5 = 2/5 book

P : 2/5 book --> 5 h
4/25 book --> 4/25 x 5/2 x 5 = 2 h
1 book --> 5/2 x 5 = 12 1/2 h

a) It was 2 h.

b) It was 12 1/2 h

Hi all,

The above question is from Maha Bodhi 2010 P6 Prelim Paper 2 Qn 11, solution was posted in this link http://psle2010a.blogspot.com/2010/09/maha-bodhi-p6-prelim-2010-paper-2q11.html

but I don't understand the step 1 - 3/5 = 2/5 book, can someone please help ?? :?

When both Machines P and Q are used, a book can be printed in 5 hours.



Thank you.[/quote]
Hi,

See underlined.

[atutor2001]

YLH88:

Q : 8 1/3 h --> 1 book
7 h --> 7 x 3/25 = 21/25 book
5 h --> 5 x 3/25 = 3/5 book

1 - 21/25 = 4/25 book

1 - 3/5 = 2/5 book

P : 2/5 book --> 5 h
4/25 book --> 4/25 x 5/2 x 5 = 2 h
1 book --> 5/2 x 5 = 12 1/2 h

a) It was 2 h.

b) It was 12 1/2 h

Hi all,

The above question is from Maha Bodhi 2010 P6 Prelim Paper 2 Qn 11, solution was posted in this link http://psle2010a.blogspot.com/2010/09/maha-bodhi-p6-prelim-2010-paper-2q11.html

but I don't understand the step 1 - 3/5 = 2/5 book, can someone please help ?? :?

Thank you.

Hi,
I find the solution not suitable for P6. Anyway, the reasoning is as follows :

Under normal situation
Fraction of book printed by machine Q = 3/5 of the book (in 5 hours)
so the remaining fraction must be printed by machine P : 1 - 3/5=2/5 of the book (also in 5hrs)

This gives the relationship that P can print 2/5 of the book in 5 hours.

So with the \"breakdown\" Q has printed a total of 21/25 of the book. The remaining 4/25 of the book must have been printed by P before it broke down.... we can find the time P has been printing before it breaks down.

[kancheongmum]

YLH88:

[quote]When both Machines P and Q are used, a book can be printed in 5 hours. When printing a book, Machine P broke down. As a result, it took 7 hours to complete the printing of the book. If it would take Machine Q 8 hours 20 minutes to print the book alone, (a) how long was Machine P used before it broke down? (b) how long would it take to print the book using only Machine P? [4 marks][Answer given: 2 hours before, 12½ h]



Q : 8 1/3 h --> 1 book
7 h --> 7 x 3/25 = 21/25 book
5 h --> 5 x 3/25 = 3/5 book

1 - 21/25 = 4/25 book

1 - 3/5 = 2/5 book

P : 2/5 book --> 5 h
4/25 book --> 4/25 x 5/2 x 5 = 2 h
1 book --> 5/2 x 5 = 12 1/2 h

a) It was 2 h.

b) It was 12 1/2 h

Hi all,

The above question is from Maha Bodhi 2010 P6 Prelim Paper 2 Qn 11, solution was posted in this link http://psle2010a.blogspot.com/2010/09/maha-bodhi-p6-prelim-2010-paper-2q11.html

but I don't understand the step 1 - 3/5 = 2/5 book, can someone please help ?? :?

Thank you.[/quote]Hi YLH88

In 5h Machine P print (1 - 3/5 ) = 2/5 of the book, 3/5 is done by Machine Q

You may want to look at the solution done by my DS. For rates question I always want him to list out all the info and change the work done by each individual to 1h, 1 day, 1min etc

Machine P and Machine Q --- 5 hours -----1 book
1 hour --- 1/5 book (5/25)

Machine Q ---- 8h 20 min (25/3 h) --- 1 book
1 hour --- 3/25 book

Machine P ---- 1 hour ---- 5/25 - 3/25 = 2/25 book

Machine Q ---- 7 hours ---- 3/25 x 7h = 21/25 book
work done by Machine P ---- 25/25 - 21/25 = 4/25 book

(a) 4/25 divide by 2/25 = 2hours


Machine P 2/25 book ----1 h
1/25 book ----1/2 h
1 book ----25/25 book --- 1/2h x 25 = 12.5 hours

Hope this help

[YLH88]

Hi Tang, atutor2001, kancheongmum,


Thank you so much for the explanation. Now I understood liao

[Hifive]

Hi Brenda 10 and VC’s mum


Thanks so much for the solutions to my questions.

Regards

[Hifive]

Vanilla Cake:

Hifive:

1) A class was fixing a puzzle of their photos. In the first hour, the ratio of the number of fixed pieces to unfixed pieces is 1:5. In the next hour, they fixed another 15 pieces of the puzzle. Finally, the number of fixed pieces became 60% of the unfixed pieces. How many pieces were there in the puzzle?

This question is from Catholic High School (Primary) 2009 P5 SA2 Paper 2 Q10 [3 marks]

DD2's workings
Before
F : UF
1 : 5
4 : 20

After
F : UF
3 : 5
9 : 15

5u=15
24u=72

Number of pieces in the puzzle was 72

VC's mum

Hi VC's mum

can you pls explain why you change the \"before\" to 4:20 and \"after\" to 9:15?

Thanks in advance.

[Hifive]

Brenda10:

Hifive:

Hi everyone


Need help on the following questions:

1) A class was fixing a puzzle of their photos. In the first hour, the ratio of the number of fixed pieces to unfixed pieces is 1:5. In the next hour, they fixed another 15 pieces of the puzzle. Finally, the number of fixed pieces became 60% of the unfixed pieces. How many pieces were there in the puzzle?


Source : Catholic High SA2 2009 P5

Thanks in advance.

Working:
60/100 = 3/5


At First
Fixed unfixed
1 5
x8 x8
8 40

At End
Fixed Unfixed
3 5
x6 x6
18 30

18 - 8 = 10 units and 40 - 30 = 10 units


10 units = 15
1 unit = 1.5
48 units = 48 x 1.5 = 72

Thank you.

Hi Brenda 10

The method you use is different from VC's mum but both got the same answer. I am trying to study the 2 methods and explain both ways to my DS. Could you pls explain why you multiply \"at first\" by 8 and \"at end\" by 6?

Thanks in advance.

[Brenda10]

Hifive:

Brenda10:

[quote=\"Hifive\"]Hi everyone


Need help on the following questions:

1) A class was fixing a puzzle of their photos. In the first hour, the ratio of the number of fixed pieces to unfixed pieces is 1:5. In the next hour, they fixed another 15 pieces of the puzzle. Finally, the number of fixed pieces became 60% of the unfixed pieces. How many pieces were there in the puzzle?


Source : Catholic High SA2 2009 P5

Thanks in advance.

Working:
60/100 = 3/5


At First
Fixed unfixed
1 5
x8 x8
8 40

At End
Fixed Unfixed
3 5
x6 x6
18 30

18 - 8 = 10 units and 40 - 30 = 10 units


10 units = 15
1 unit = 1.5
48 units = 48 x 1.5 = 72

Thank you.

Hi Brenda 10

The method you use is different from VC's mum but both got the same answer. I am trying to study the 2 methods and explain both ways to my DS. Could you pls explain why you multiply \"at first\" by 8 and \"at end\" by 6?

Thanks in advance.[/quote]Hi Hifive

Since the total number of puzzles remains the same, we must make the total numbers of puzzle the same by using common multiple. As such the \"At First\" and \"At End\" is 48 units.

Note: 6 is taken from At First : 1 + 5
8 is taken from At End : 3 + 5

BTW, I find VC's mum method easier, you may want to consider using this after her explanation.

Thank you.

[Vanilla Cake]

Brenda10:

Hi Hifive


Since the total number of puzzles remains the same, we must make the total numbers of puzzle the same by using common multiple. As such the \"At First\" and \"At End\" is 48 units.

Note: 6 is taken from At First : 1 + 5
8 is taken from At End : 3 + 5

BTW, I find VC's mum method easier, you may want to consider using this after her explanation.

Thank you.

Hi Brenda10,

Thks for helping to explain to Hifive, my mum and I also have difficulties in understanding my younger sister's P5 Maths workings. Too many shortcuts and will eventually lead to her downfall in 2011 PSLE Maths exams .