Hard maths question (2 Viewers)

[wantingtoknow]

1) A bus and a truck left town A at 10.00am and went along the road between towns A and B at constant speeds. At the same time, a car set off from B along the same road at a constant speed. The car first met the truck 30*** minutes later and then after 10 more minutes it met the bus. The truck reached B, immediately turned back and, on its way to A, met the bus 2 hours since it left A. When will the truck get back to A?

2) A student rows at a constant speed (relative to the water) downstream in the Nambucca River from Bowraville to Macksville in 3 hours and back upstream in 4 hours. If the river flows at a constant rate, find the number of hours it would take a piece of driftwood to float downstream from Bowraville to Macksville.

3) (Is it possible to work this question out with simultaneous equations and how?) A certain integer is between 10 and 100. Its value is 8 times the sum of its digits and if it is reduced by 45, its digits are reversed. Find the integer.

 

[nightweaver066]

3 was fun.

I used simultaneous equations (had to force myself to remember little rules i set so that i don't get them mixed up) and i ended up with 72.







































Although you can just use the first generated equation,



and notice how X must be integral, so Y = 2, 4, 6, 8, ...

Test the first value for Y and you get the answer as well haha.

 

[wantingtoknow]

what equations did you come up with for that question? :O

 

[nightweaver066]

what equations did you come up with for that question? :O

Updated post.

 

[wantingtoknow]

thank youuuu! I didn't think it was possible to do it with simultaneous equations.

 

[kazemagic]

lol... question 3 was taken from cambridge just did it today when i was cramming all my homework. I don't know a way without using simultaneous tho

 

[RealiseNothing]

lol... question 3 was taken from cambridge just did it today when i was cramming all my homework. I don't know a way without using simultaneous tho

You could use inspection pretty easily:

Notice that when you subtract 45 it's digits are reversed?

Well the 9 times tables go up, and eventually the digits just reverse as well right? 09, 18, 27, 36, 45, 54, 63, 72, 81, 90.....

And since 45 is part of the 9 times tables, the answer is also going to be part of the 9 times tables.

We know that it is 8 times the sum of it's digits, but remember that all 9 times tables have a sum of their digits of 9 yer? So we just do 9 times 8 which gets us 72.

 

[wantingtoknow]

lol... question 3 was taken from cambridge just did it today when i was cramming all my homework. I don't know a way without using simultaneous tho

Which cambridge book?

 

[kazemagic]

3u Year 11

 

[wantingtoknow]

3u Year 11

do you know which chapter/exercise it is it?

 

[bleakarcher]

Is the first one 12pm?

 

[wantingtoknow]

answer is 12:40pm D:

 

[kazemagic]

In chapter 1H Q4,H lol which is basically revision of yr9 and 10.

lol Realise, I kinda get ur explanation but I just dont understand how do you limit the answer down to be in the 9 timetables just because it gets subtracted by 45

 

[RealiseNothing]

Is the first one 12pm?

This is the answer to the first one.

 

[wantingtoknow]

This is the answer to the first one.

no, the answer is 12:40pm ;[

 

[RealiseNothing]

no, the answer is 12:40pm ;[

Answers are wrong then.

It's definately 12pm.

 

[bleakarcher]

When the truck reverses direction does it continue to travel at the same constant speed?

 

[wantingtoknow]

Answers are wrong then.

It's definately 12pm.

do you want to justify why you think that then? :O

When the truck reverses direction does it continue to travel at the same constant speed?

yep

 

[RealiseNothing]

The car reaches the truck after 20 minutes, and the bus after 30 minutes. Let the distance between where the car meets the truck and where it meets the bus be .

So it takes the car 10 minutes to travel a distance of .

But it took the car 20 minutes to reach the truck in the first place, so the distance from town B to where the car met the truck is .

Hence from town B to where the car meets the bus is .

Now let the distance from town A and where the car meets the bus be some unknown distance .

So the distance from town A to town B is .

In 30 minutes, the bus travels the distance , whilst the truck travels in 20 minutes.

Equate both to 30 minutes:

Bus -
Truck -

Hence after every 30 minutes, the truck travels a distance of more than the bus.

The truck meets the bus after two hours, so it will be a distance of in front of the bus. Which simplifies to , and simplifying more gives .

But we know that the distance from town A to town B is .

Hence the distance from town A to town B and back is .

So the truck actually meets the bus after travelling the distance from town A to town B and back again. It does this in 2 hours as stated before.

So the bus is actually not even moving lol.

 

[wantingtoknow]

okay, I'm so sorry. my friend just told me she did a typo in her question. >_<
it's 30 minutes, not 20 minutes.