Q&A - PSLE Math

[Despair]

MathIzzzFun:

Despair:

Dear all, I require help with this Speed question.


A truck started its journey from Village Tiku to Village Chuka at 16 30. At the same time, a bus started travelling from Village Chuka to Village Tiku.

The ratio of the truck's speed to the bus's speed is 8:3. At 17 00 the two vehicles passed each other. The truck increased its speed and reached Village Chuka at 17 20 while the bus increased its speed by 18km/h.

When the truck reached Village Chuka, the bus is still 40 km away from Village Tiku.

What is the distance between the two villages?

Thank you in advance.

Hi

May I know the source of this problem sum? The setter probably adapted the problem by changing the numbers..firstly, after the truck and bus passed each other, the truck reduced its speed rather than increased its speed because if it had continued at original speed, it would hve reached the destination in 3/8 x 30min = 11.25min.

Ratio of distance travelled by truck n bus = 8u : 3u, total distance 11u.

after truck and bus passed each other, truck took 20 min to reach Chuka,and the bus is still 40 km from Tiku.

If bus had continued its original speed, the distance it would travel = 20/30 x 3u =2u, since the bus's speed is increased by 18km/h, it would travel 18x20/60 = 6km more, ie it travelled a distance of 2u + 6km after passing the truck, and it was 40km from Tiku.

Distance from Tiku to the \"meeting point\" = 8u
8u = 2u + 6km + 40km, 6u = 46km, 11u = 11/6 x 46 km = 84 1/3 km
Distance between Tiku and Chuka = 84 1/3 km.

cheers.

Hi, sorry, I do not know the source But I think it must be from some Preliminary Paper. This was a question from my teacher. I will check with her tomorrow and get back to you.

Thank you once more for solving my question.

[MathIzzzFun]

nanosphere:

pls help me with this question :?:


Andy, billy and charlie cycled at the same time from point X towards another cyclist ahead of them. Andy, billy and charlie took 6 minutes,10 minutes and 12 minutes respectively to overtake the cyclist. Andy's speed was 25km/h and billy's speed was 21km/h.
(a) How far was billy from point X when he overtook the cyclist?

(b) What was Charlie's cycling speed?

:thankyou:

Hi

this one would be quite easily solved using \"area\" method.. here's the usual method ..

a) Billy's distance from X = 10min x 21km/h = 3.5km

When Andy caught up with the cyclist, distance travelled by Andy = 6min x 25km/h = 2.5km
At this time, Billy travelled 6min x 21 km/h = 2.1km.
So, 6min after they started cycling, Billy is 2.5km - 2.1km = 0.4km behind the cyclist.

Billy caught up with the cyclist after cycling for 10 min ie 4 min after Andy caught up with the cyclist.
0.4km/4min= 6km/h so Billy is cycling 6km/h faster than the cyclist ie
cyclist's speed = 21km/h - 6km/h =15km/h

Billy took 10min to catch up with the cyclist, 10min x 6km/h = 1km ie the cyclist was 1km ahead when Andy, Billy and Charlie started cycling.

Charlie took 12min to make up 1km, 1km/12min = 5km/h ie Charlie was cycling 5km/h faster than the cyclist.

Charlie's speed = 15km/h + 5km/h = 20 km/h

cheers.

[Cheerfuldad]

Hi all,


Please help on the following question:

Jason, Edward and Sam had a total of $837. Jason had the least amount of money. The ratio of Edward’s money to Sam’s money was 4:3 at first. Jason and Edward each spent 1/3 of their money. Given that the three boys had $648 left, how much did Jason have at first?

TIA

[MathIzzzFun]

Cheerfuldad:

Hi all,


Please help on the following question:

Jason, Edward and Sam had a total of $837. Jason had the least amount of money. The ratio of Edward's money to Sam's money was 4:3 at first. Jason and Edward each spent 1/3 of their money. Given that the three boys had $648 left, how much did Jason have at first?

TIA

Hi

$837 - $648 = $189
So 1/3 of Jason & Edward's money = $189
Jason and Edward had a total of 3 x $ 189 = $ 567
Amount that Sam had = $837 - $ 567 = $ 270
Total amount Edward and Sam had = 7/3 x $ 270 = $630

Amount Jason had at first = $ 837 - $ 630 = $207

cheers.

[tianzhu]

spunky:

Thanx so much for ur help.

Hi

Good Morning.

You’re welcome.

Best wishes

[tianzhu]

ozora:

Thanks tianzhu. it really helps. It unblocks my mental brain. THanks thanks

Hi

Good Morning.

You’re welcome.

Best wishes

[PiggyLalala]

MathIzzzFun:

nanosphere:

pls help me with this question :?:


Andy, billy and charlie cycled at the same time from point X towards another cyclist ahead of them. Andy, billy and charlie took 6 minutes,10 minutes and 12 minutes respectively to overtake the cyclist. Andy's speed was 25km/h and billy's speed was 21km/h.
(a) How far was billy from point X when he overtook the cyclist?

(b) What was Charlie's cycling speed?

:thankyou:

Hi

this one would be quite easily solved using \"area\" method.. here's the usual method ..

a) Billy's distance from X = 10min x 21km/h = 3.5km

When Andy caught up with the cyclist, distance travelled by Andy = 6min x 25km/h = 2.5km
At this time, Billy travelled 6min x 21 km/h = 2.1km.
So, 6min after they started cycling, Billy is 2.5km - 2.1km = 0.4km behind the cyclist.

Billy caught up with the cyclist after cycling for 10 min ie 4 min after Andy caught up with the cyclist.
0.4km/4min= 6km/h so Billy is cycling 6km/h faster than the cyclist ie
cyclist's speed = 21km/h - 6km/h =15km/h

Billy took 10min to catch up with the cyclist, 10min x 6km/h = 1km ie the cyclist was 1km ahead when Andy, Billy and Charlie started cycling.

Charlie took 12min to make up 1km, 1km/12min = 5km/h ie Charlie was cycling 5km/h faster than the cyclist.

Charlie's speed = 15km/h + 5km/h = 20 km/h

cheers.

Hi MathIzzzFun,
I am interested in the easy 'area' method to solve this question. Would you mind posting the solution here too? Thank you very much.

[tianzhu]

nanosphere:

Andy, billy and charlie cycled at the same time from point X towards another cyclist ahead of them. Andy, billy and charlie took 6 minutes,10 minutes and 12 minutes respectively to overtake the cyclist. Andy's speed was 25km/h and billy's speed was 21km/h.
(a) How far was billy from point X when he overtook the cyclist?
(b) What was Charlie's cycling speed?

Hi

Hope this helps.

Best wishes

http://farm7.static.flickr.com/6181/6122457080_e81c3e1c29_z.jpg\">

[Cheerfuldad]

Hi MathIzzzFun,


Thank you for your help!

Cheers!

MathIzzzFun:

Cheerfuldad:

Hi all,

Please help on the following question:

Jason, Edward and Sam had a total of $837. Jason had the least amount of money. The ratio of Edward's money to Sam's money was 4:3 at first. Jason and Edward each spent 1/3 of their money. Given that the three boys had $648 left, how much did Jason have at first?

TIA

Hi

$837 - $648 = $189
So 1/3 of Jason & Edward's money = $189
Jason and Edward had a total of 3 x $ 189 = $ 567
Amount that Sam had = $837 - $ 567 = $ 270
Total amount Edward and Sam had = 7/3 x $ 270 = $630

Amount Jason had at first = $ 837 - $ 630 = $207

cheers.

[michyms]

In today’s Forum, someone wrote in about a maths question in a prelim paper: Three halls contained 9,876 chairs altogether. One-fifth of the chairs were transferred from the first hall to the second hall. Then, one-third of the chairs were transferred from the second hall to the third hall and the number of chairs in the third hall doubled. In the end, the number of chairs in the three halls became the same. How many chairs were in the second hall at first?


Can anyone enlighten how this is done?