Welcome to Test-paper.info
Tuesday, January 16 2018 @ 03:04 PM CST
 Select a Forum » General Chat » Primary 1 Matters » Primary 2 Matters » Primary 3 Matters » Primary 4 Matters » Primary 5 Matters » Primary 6 Matters » Question, Feedback and Comments » Education Classified
 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 1394 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

Newbie

Registered: 06/23/09
Posts: 8

 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

Active Member

Registered: 04/21/11
Posts: 627

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

Thank you very much for the prompt and succint answer.

Ted

Newbie

Registered: 06/23/09
Posts: 8

 All times are CST. The time is now 03:04 pm.
 Normal Topic Locked Topic Sticky Topic
 New Post Sticky Topic w/ New Post Locked Topic w/ New Post
 View Anonymous Posts Able to Post HTML Allowed Censored Content