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 By: acelow (offline)  Tuesday, September 10 2013 @ 09:13 AM CDT (Read 674 times)
acelow

Tanya and Philip ran the same distance. Tanya started her run 10 minutes before Philip and finished 5 minutes before Philip. When Tanya finished running, Philip had completed 5/6 of the distance and still had 1km to go. Find their respective speeds. Leave your answers in term of km/h.

Pls help again!
Thank you!

Newbie

Registered: 05/02/09
Posts: 14

 By: echeewh (offline)  Tuesday, September 10 2013 @ 09:50 PM CDT
echeewh

Hi <acelow>,

Following is my worked solution:

*** - for alignment purpose

A *********************************** B
|-------|-------|-------|-------|-------|-------|
|-> ****** |-> ***************** |-> ** |->
P ******* T ****************** P1 ** T1

t(PT) = 10 mins = (10/60) = (1/6) hr
t(P1B ) = 5 mins = (5/60) = (1/12) hr
d(P1B ) = 1 km
d(AB ) = 6 km

hence, s(P) = d(P1B ) ÷ t(P1B )
= 1 ÷ (1/12) = 12 km/h

Given that when T finished running (T1), P had completed 5/6 of the distance (P1),
t(TT1) = t(PP1)

t(PP1) = d(PP1) ÷ s(P)
= 5 ÷ 12 = (5/12) hr = t(TT1)

so, t(AT1) = t(TT1) + t(AT) {since T started 10 mins earlier}
= (5/12) + (1/6) = (7/12) hr

s(T) = 6 ÷ (7/12) = 6 × (12/7)
= (72/7) = 10 2/7 km/h

========

Trust this helps.

Do let me know again if this is different from your <Answerkey> or if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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