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 Rosyth School Prelim 2012 Qn 18 (speed)
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By: acelow (offline)  Monday, August 05 2013 @ 07:54 AM CDT (Read 2736 times)  
acelow

Two buses X and Y left ABC interchange at 6.35a.m. to pick up passengers.
They travelled at an uniform speed in opposite directions round a 55km circular route.
Bus X took 50minutes to complete each round.
After every 30 minutes, the two buses would meet.
At what time would the two buses meet at the interchange again?
(Ans: 9.05am)

kindly help again... thank you Smile


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By: echeewh (offline)  Monday, August 05 2013 @ 09:17 PM CDT  
echeewh

Hi <acelow>

Following is my worked solution :


X:
50 mins per round of 55 km.
sX = 55 ÷ (50/60) = 55 × (6/5) = 66 km/h

X, Y met every 30 mins.
In this duration of 30 mins, X travelled 33 km, while Y travelled 22 km to meet. { based on the circular route of 55 km }

Hence, sY = 22 ÷ (1/2) = 44 km/h

Using <Common Time> method, where distance ratio is the same as speed ratio.

sX : sY
66 : 44
6 : 4
3 : 2

dX : dY
3 : 2

dX + dY = 5u = 1 round of the circular route of 55 km

In order for X, Y to meet at the interchange, each would have to travel a multiple of 5u of the circular route.

Following are X,Y meeting points (based on unit distance travelled)

X: 3u 6u 9u 12u 15u 18u
Y: 2u 4u 6u 8u 10u 12u

At the 5th meeting point, note that both X,Y travelled a multiple of 5u (the circular route). X travelled 15u, while Y travelled 10u of the circular route. And both would meet at the starting point (interchange).

As each meeting point takes 30 mins, the 5th meeting point (at interchange) would take ...

5 × 30 = 150 mins = (5/2) hrs

Given that both X,Y first started from interchange at 06 35,

time to meet (at interchange) = 06 35 + 2 30
= 09 05 = 9.05 am

=========

Trust this helps.

Do let me know again if there's further clarification.

Cheers,
Edward

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By: acelow (offline)  Wednesday, August 28 2013 @ 09:03 AM CDT  
acelow

I don't quite understand why do we need to use the multiple of 5 that leads us to X travelling 15u and Y travelling 10u.

Kindly help as I couldn't find the answer from any of my peers and teachers.

Thank you! Big Grin

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By: echeewh (offline)  Wednesday, August 28 2013 @ 03:38 PM CDT  
echeewh

Hey <acelow>,

The question is about a circular route that is 5u distance long. You are also given that both buses X,Y started from the interchange and they would meet after every half hour.

Logically if both buses were to meet at the interchange again, their meeting point must be at a position in which X, Y have each made (or travelled) a multiple of 5u (i.e. 1 complete round of the circular route).

Lets revisit X,Y meeting points (based on unit distance travelled)

X: 3u 6u 9u 12u 15u 18u
Y: 2u 4u 6u 8u 10u 12u

If you refer to their 2nd meeting point in which X travelled 6u and Y travelled 4u, X would already be past (out of) the interchange (1u distance past interchange) and Y would be approaching the interchange (1u distance away). Thus, X,Y did not meet at the interchange.

Same reasoning goes for their 3rd and 4th meeting points.

However, at the 5th meeting point, both X,Y would be at the interchange as X completed 3 rounds and Y completed 2 rounds of the same circular route starting from the interchange.

Draw a picture (or model) for your own illustration and understanding. Believe that will help further.

**If not, I strongly encourage you to come for my PSLE intensive revision course that has just started this week Big Grin

=========

Trust this clarifies.

Cheers and all the best,
Edward

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By: MathIzzzFun (offline)  Wednesday, August 28 2013 @ 05:37 PM CDT  
MathIzzzFun

Quote by: acelow

Two buses X and Y left ABC interchange at 6.35a.m. to pick up passengers.
They travelled at an uniform speed in opposite directions round a 55km circular route.
Bus X took 50minutes to complete each round.
After every 30 minutes, the two buses would meet.
At what time would the two buses meet at the interchange again?
(Ans: 9.05am)

kindly help again... thank you Smile




this is a question on common multiple...

X took 50 min to complete each round --> X will be at the interchange every 50 min
X and Y would meet every 30 min --> to find the next time to meet, find the common multiple of 50 and 30 --> 150
X and Y would meet again after 150 min = 2h 30 min
6.35am + 2h 30min --> 9.05 am

cheers.

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By: acelow (offline)  Thursday, August 29 2013 @ 08:27 AM CDT  
acelow

Quote by: echeewh

Hey <acelow>,

The question is about a circular route that is 5u distance long. You are also given that both buses X,Y started from the interchange and they would meet after every half hour.

Logically if both buses were to meet at the interchange again, their meeting point must be at a position in which X, Y have each made (or travelled) a multiple of 5u (i.e. 1 complete round of the circular route).

Lets revisit X,Y meeting points (based on unit distance travelled)

X: 3u 6u 9u 12u 15u 18u
Y: 2u 4u 6u 8u 10u 12u

If you refer to their 2nd meeting point in which X travelled 6u and Y travelled 4u, X would already be past (out of) the interchange (1u distance past interchange) and Y would be approaching the interchange (1u distance away). Thus, X,Y did not meet at the interchange.

Same reasoning goes for their 3rd and 4th meeting points.

However, at the 5th meeting point, both X,Y would be at the interchange as X completed 3 rounds and Y completed 2 rounds of the same circular route starting from the interchange.

Draw a picture (or model) for your own illustration and understanding. Believe that will help further.

**If not, I strongly encourage you to come for my PSLE intensive revision course that has just started this week Big Grin

=========

Trust this clarifies.

Cheers and all the best,
Edward



Is it a tuition? If it is, how much is it and where is it?

Thank You Smile

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By: echeewh (offline)  Thursday, August 29 2013 @ 11:54 AM CDT  
echeewh

Hey <acelow>,

Please kindly refer to my posts in this Forum as indicated below:

Forum Index > Miscellaneous > Education Classified > UPGRADE YOURSELF TO A WHOLE NEW LEVEL

Forum Index > Miscellaneous > Education Classified > Achieving good Results in Primary Maths

======

Thank you ...& all the best in your PSLE,

Cheers,
Edward

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