Sign Up!
Login
Welcome to Test-paper.info
Friday, August 18 2017 @ 07:48 AM CDT
 Forum Index >  Test Paper Related >  Primary 6 Matters
 P6 speed question
   |  Printable Version
By: ycthun (offline)  Saturday, July 28 2012 @ 10:12 PM CDT (Read 1318 times)  
ycthun

Hi.

I need help with this question. Can anyone help. Thanks

At 0900hr, John started cycling from point A to point B.  At the same time, Mary started cycling from Point B to point A using the same route.  Cycling at a speed of 4km/hr faster than Mary, John met up with Mary 300m from the midpoint.

a.  At what time did the two meet?

b.  if John took another 3 mins to reach point B, at what time will Mary reach point A?

Ted

Forum Newbie
Newbie

Registered: 06/23/09
Posts: 8

Profile Email    
   
By: echeewh (offline)  Sunday, July 29 2012 @ 10:00 PM CDT  
echeewh

Hey Ted,

Following pls find my worked solution :

P - Midpoint
X - where J,M would meet

A **************** P ****** X ******* B
|-----------------------|----------|-----------|
|-> *************** <300m> ***** <-|
J ************************* |-> ***** M
S(J)=S(M) + 4 ********* <-|
************************ (J1,M1)


Notes:
If J were to cycle at the same speed as M, both would be 300 m away from the midpoint P, i.e. distance apart/separating each other = 600 m.
The extra speed of 4 km/hr by J would take him to meet M at X, which is 300 m from P. (refer distance-time model (J1,M1))

(a)

Time taken to meet at X = (Distance apart) ÷ (Speed Difference)

= 0.6 ÷ 4 = 0.15 hr = 9 mins

As both J,M started at 0900, both met at 0909

(b)

Given that J took another 3 mins to reach B,

Dist (XB ) covered by J = [(S(M) + 4) x (3/60)]

This is the same distance travelled by M in 9 mins, which is ...

Dist (BX) coverd by M = S(M) x (9/60)

So we have ...
[(S(M) + 4) x (3/60)] = S(M) x (9/60)
3 S(M) + 12 = 9 S(M)
9 S(M) - 3 S(M) = 12
6 S(M) = 12
S(M) = 2 km/h

S(J) = S(M) + 4 = 2 + 4 = 6 km/h
Dist AB = 6 x (12/60) = 1.2 km

Time taken by M to reach A = 1.2 ÷ 2 = 0.6 hr = 36 mins

Time at which M reached A = 0936

===========================

Trust this helps.

Do let me know again if these do not agree with your Answerkey or if there's any clarification.

Cheers,
Edward

Forum Active Member
Active Member

Registered: 04/21/11
Posts: 625

Profile Email    
   
By: ycthun (offline)  Sunday, July 29 2012 @ 10:13 PM CDT  
ycthun

Thank you very much for the prompt and succint answer.

Ted

Forum Newbie
Newbie

Registered: 06/23/09
Posts: 8

Profile Email    
   


 All times are CDT. The time is now 07:48 am.
Normal Topic Normal Topic
Locked Topic Locked Topic
Sticky Topic Sticky Topic
New Post New Post
Sticky Topic w/ New Post Sticky Topic w/ New Post
Locked Topic w/ New Post Locked Topic w/ New Post
View Anonymous Posts 
Able to Post 
HTML Allowed 
Censored Content