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TSD doubt
by RUPALI GOYAL - Friday, 31 October 2014, 07:27 AM
  Hero and Hercules start simultaneously from P towards Q. when the distance between Hero and Hercules was 30km, champ starts frpm P to Q. The distance travelled by Champ to overtake Hercules is twice the distance he travelled to overtake Hero. The ratio of speeds of Hercules and Hero is 3:2.

1. what is ratio of speed of Champ to that of Hero?
a. 4:1
b. 3:1
c. 2:1
d. none of these

2. what is the distance between Hero and Hercules when Champ was equidistant from Hero and Hercules?
a. 45
b. 48
c. 51 3/7
d. cannot be determined
Re: TSD doubt
by Raghav Lakhotia - Saturday, 1 November 2014, 11:06 AM
  1) b ? (3:1)
Re: TSD doubt
by Raghav Lakhotia - Saturday, 1 November 2014, 11:10 AM
  2) c (360/7) ?
Re: TSD doubt
by RUPALI GOYAL - Saturday, 1 November 2014, 11:34 AM
  Raghav, both of your ans are correct. could yo please explain the solutions. I have solved it in following way and I am getting 4:1 as my ans.

P---------------------R-------------------------S----------------Q
P<-----d------>  Hero <-----30km----->Hercules
C starts

let speed of Hero=a
speed of Hercules=b
Speed of champ=c

b/a=3/2

the time in which Hero covers d distance, Hercules covers d+30.

b/a=d+30/d=3/2, solving this d=60km

since Champ travels twice the distance to catch Hercules than to catch Hero.

therefore, the time in which champ catches hero, hercules is travelling moving ahead 30km

relative speed of champ w.r.t hero =c-a
time=60/c-a

in this time, hercules must have travelled 30 km so that now the champ has to travel further disatnce of 60km to catch hercules and hence the total distance by champ becomes twice.

(60/c-a)b=30
60b/c-a=30
2b/c-a=1
3a/c-a=1  (b/a=3/2)
3a=c-a
c/a=4:1

could you please tell me what is wrong in this ?

I could not solve 2nd question.

Please explain your approach.




Re: TSD doubt
by Raghav Lakhotia - Saturday, 1 November 2014, 11:40 AM
  Hello Rupali
d=60...correct
hence herculi travelled 90 and hero 60
now champ overtakes
to overtake herculi time required = 90/(c-3k)
to overtake hero, time required = 60/(c-2k)
and
90/(c-3k) = 2*60/(c-2k)
hence
3c-6k = 4c-12k
hence
c = 6k
therefore ratio = 6:2 = 3:1 smile

for next question, let time be t at the required moment
90 + 3kt - 6kt = 6kt -60 - 2kt
t = 150/7k
in this time distance between hero and herculi is
30(initial) + 150/7 = 360/7 smile
Re: TSD doubt
by RUPALI GOYAL - Saturday, 1 November 2014, 11:48 AM
  Thanks a lot Raghav. smile I understood error in my approach.