Problems - Hard! ASAP! (1 Viewer)

[michael11]

Hey, I was wondering if anyone knew how to answer these questions because I am not really sure.

Question 1 - If Pirate Pete can unload a treasure chest in five minutes and Peg Leg can unload the same chest in two and a half minutes, how long will it take them both to empty it working together?

Question 2 - A man travelled 10, 000 kilometres in a car with one spare tyre. He rotated tyres at intervals so that when the trip ended each tyre has been used for the same number of kilometres. For how many kilometres was each tyre used?


THANKYOU!

 

[Mountain.Dew]

Hey, I was wondering if anyone knew how to answer these questions because I am not really sure.

Question 1 - If Pirate Pete can unload a treasure chest in five minutes and Peg Leg can unload the same chest in two and a half minutes, how long will it take them both to empty it working together?

Question 2 - A man travelled 10, 000 kilometres in a car with one spare tyre. He rotated tyres at intervals so that when the trip ended each tyre has been used for the same number of kilometres. For how many kilometres was each tyre used?


THANKYOU!

Michael11, welcome to the BOS forums!

here is my 2 cents for doing q1)

my logic goes as follows:

in one minute, pete can unload 1/5 of treasure.
in one minute, Peg Leg can unload 2/5 of the treasure.

so working together, if they worked for one minute, they would get (1/5 + 2/5) of the treasure unloaded

for 2 mins...(1/5 + 2/5)(2) treasure unloaded

so and so forth...so, for N mins, they unload (1/5 + 2/5)(N) of treasure.

so, the general formula would be: (1/5 + 2/5)(N) = 1

now, find N, in minutes.

 

[icycloud]

Q1) dp/dt = 1/5, dq/dt = 2/5, dp/dt + dq/dt = 3/5, thus 5/3 minutes to unload the treasure
Q2) 5x = 40000, x = 8000 km per tyre travelled

 

[SoulSearcher]

Its been so long since year 9 that I almost forgot how to do these types of questions.

btw Mountain.Dew I think there's a typo in your working out.

 

[michael11]

So which answer is right for q1? I worked out 1/1/4 (1 minute 15 seconds) yet the answer you say is 5/3.
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[icycloud]

michael, please show us your working, how did you get 5/4?

 

[michael11]

i followed Mountain Dew's general formula. (1/5 + 3/5)(N)=1
Find N in minutes.
So 4/5 x N = 1
N= 1 divide by 4/5
N= 1/1/4
=1minute 15 seconds
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[icycloud]

I think he made a typo. It's mean to be (1/5 + 2/5)n=1

 

[michael11]

thanks. So it would be 1minute 40 seconds? Also, so it is 8000km for each tyre? Could you please show a bit more working, i don't really understand. Thanks.
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[michael11]

Thanks i figured out the tyre one. It does work out to be 8000km.
I have one more question if you wouldn't might helping.

In a stationary store, pencils have one price and pens have another price. Two pencils and three pens cost 78c; but three pencils and two pens cost 72c. How much does one pencil cost?

Thankyou.
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[icycloud]

Let p = cost of pencil, q = cost of pens

2p + 3q = 78 --- equation 1
3p + 2q = 72 --- equation 2

From equation 1:

q = (78-2p)/3

Substitute into equation 2:
3p + 2(78-2p) /3 = 72
9p + 156 - 4p = 216
5p = 60
p = 12, q = 18

Therefore, pencils cost 12c and pens cost 18c.

 

[michael11]

thankyou

 

[michael11]

Hi everyone. i was wondering if you could help me out or give me some hintsagain with some questions. I am having some trouble figuring them out. Thanks.

Question 1

My watch loses one minute every hour, while your watch gains one minute every hour. If they both show 12 noon now, when will they again show the same time?

Question 2

A 60 km/h train takes 6 seconds to pass a man standing on a station. How long is the train?

Question 3

If two dogs ate 6 cans of pet food in two days, how many cans of pet food would 3 dogs eat in 4 days?

Question 4

What number less than 100, has two factors, its digits add up to 11, and the difference between the digits is 3?

Thanks guys.

 

[Riviet]

Q2

60km/h = (60 x 1000)/(60 x 60) m/s
=50/3 m/s

distance = speed x time
= 50/3 x 6
= 100 m.

 

[SoulSearcher]

Q4

47 works out, I think.

 

[Rax]

You getting everyone to do your homework? lol
I am way too tired to think of how to answer those
Good luck Michael

 

[housemouse]

This looks like year 10 questions but I cant even get them out.What topic do these questions fall under?

 

[michael11]

Just random ones.

 

[Mountain.Dew]

Its been so long since year 9 that I almost forgot how to do these types of questions.

btw Mountain.Dew I think there's a typo in your working out.

whoops...BIG BIG typo...

thank you icycloud! greatly appreciated!

now, other questions:

Hi everyone. i was wondering if you could help me out or give me some hintsagain with some questions. I am having some trouble figuring them out. Thanks.

Question 3

If two dogs ate 6 cans of pet food in two days, how many cans of pet food would 3 dogs eat in 4 days?

two dogs...6 cans...2 days...means

1 dog...3 cans...2 days...means

1 dog...6 cans...4 days...means

3 dogs...18 cans...4 days...

so, 18 cans, i would reckon. dunno if its right or not though.

 

[word.]

1. i'm assuming it's a 24 hr watch or one that displays am/pm since you mentioned it

every 30 days

in a day, watch1 elapses 59*24 = 1416 minutes
watch2 elapses 61*24 = 1464 minutes

for the watches to have identical time, they'd need a time difference of 24 hours
i.e. 1440 minutes

let n be the number of days,

1464n - 1416n = 1440
n = 30


2. 60km/h = 60000m/h = 1000m/min = 50/3 m/s
6*50/3, the train is 100m long

3. 2 dogs 6 cans 2 days -> 2 dogs 12 cans 4 days -> 3 dogs 18cans 4 days

4. let M and N be the digits,
M + N = 11, M - N = 3
M = 3 + N
3 + N + N = 11,
2N = 8, N = 4, M = 7, so 47 because 74 is not prime