
By: vivilau1112 (offline) Thursday, August 08 2013 @ 04:27 AM CDT (Read 592 times)



vivilau1112 
Hello everyone, again! I am stuck at this question.Can someone help?Much appreciated

Junior
Registered: 04/13/11 Posts: 16





By: echeewh (offline) Friday, August 09 2013 @ 05:32 AM CDT



echeewh 
Hi <vivilau1112>,
Following is my worked solution:
***  for alignment purpose

O ********************* H
> ************* >
T ************** T1
s(T1) = s(T)  20 , where s(T) is the usual speed and s(T1) is the slower speed.
Given that at this slower speed, T would arrive 10 mins later. So ...
t(T1H) = 10 mins = (1/6) hr
d(T1H) = [s(T)  20] × (1/6) = [s(T)  20] / 6
d(TT1) = 40  [s(T)  20] / 6
= {240  [s(T)  20]} / 6
= [260  s(T)] / 6
At its usual speed,
t(TH) = 40 ÷ s(T)
= 40 / s(T)
At its slower speed, this time taken is the same as t(TT1). i.e. t(TH) = t(TT1)
t(TT1) = {[260  s(T)] / 6} ÷ [s(T)  20]
= [260  s(T)] / [6s(T)  120]
Equate this ..
40 / s(T) = [260  s(T)] / [6s(T)  120]
40 [6s(T)  120] = s(T) [260  s(T)]
240s(T)  4800 = 260s(T)  [s(T) × s(T)]
[s(T) × s(T)]  260s(T) + 240s(T)  4800 = 0
[s(T) × s(T)]  20s(T)  4800 = 0
[s(T) + 60] [s(T)  80] = 0
s(T) = 60 , 80
Hence, usual speed of T = 80 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: 623





By: echeewh (offline) Friday, August 09 2013 @ 10:26 AM CDT



echeewh 
An alternative solution to this is :
At its usual speed,
t(TH) = 40 ÷ s(T)
= 40 / s(T)
At its slower speed,
t(TH) = 40 ÷ [s(T)  20]
= 40 / [s(T)  20]
Since time taken to reach home (H) at the slower speed would be 10 minutes (1/6 hr) longer, we have ...
40 / [s(T)  20]  40 / s(T) = (1/6)
{40s(T)  40[s(T)  20]} / s(T)[s(T)  20] = (1/6)
[40s(T)  40s(T) + 800] / [s(T) × s(T)]  20s(T) = (1/6)
4800 = [s(T) × s(T)]  20s(T)
[s(T) × s(T)]  20s(T)  4800 = 0
[s(T) + 60] [s(T)  80] = 0
s(T) = 60, 80
Hence, usual speed of T = 80 km/h
=========
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 623



