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A bus travelling from city A to city B breaks down midway.

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A bus travelling from city A to city B breaks down midway. [#permalink] New post 17 Aug 2004, 17:09
A bus travelling from city A to city B breaks down midway. After 30 minutes, the passengers manage to catch a taxi and reach city B IN TIME. Had the breakdown occured 30 km earlier, the passengers would have taken 37.5 minutes to catch the taxi and reach city B IN TIME. If the speed of the taxi is 20 km/hour more than that of the bus, find the speed of the bus in km/hour.
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 [#permalink] New post 17 Aug 2004, 19:34
The speed of bus is 60km/hr. I will give the detailed explanation in the next post.
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 [#permalink] New post 17 Aug 2004, 20:06
Here's my working:

Usually if the bus doesn't break down, the time taken to reach city B is x/B, where x is the distance between A and B, and B is the speed of the bus

So we are told the bus breaks down halfway, and the passesngers waited 1/2 hour for a taxi, the speed of the taxi is 20km/h and they all reached city B in x/B hours (in time), so we have
x/2B + 1/2 + x/40 = x/B
x/2B - x/40 = 1/2 ---- (1)

Now we are told the bus breaks down 30km earlier and the waiting time for a taxi is 5/8 hr so we get
(x-60)/2B = 5/8 + (x+60)/40 = x/B
(x+60)/2B - x/40 = 17/8 ---- (2)

So subtracting (1) from (2) gives

60/2B = 13/8
So B = 18.5 km.hour
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 [#permalink] New post 17 Aug 2004, 21:04
Sorry. the guest was me...forgot to log in earlier. Anyways the soln. is below

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 [#permalink] New post 17 Aug 2004, 23:43
hmm... venksune, i used the same method as you can see from my post, but somehow I haven't ended up with 60km/h. Just checked it again, this time using a calculator (not GMAT style for sure !), and still getting the same result i got earlier. I'll check again..
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 [#permalink] New post 18 Aug 2004, 03:38
Hah ! I got it now... I read the question as the speed of taxi is 20km/hr when it should be 20km/h more than the speed of the bus !! Silly me !!
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 [#permalink] New post 19 Aug 2004, 22:56
McGrath, where are all your Qs from?
I am amazed by the amount of complex equations we get.
Even thought these Qs may not seem GMATish, it is still good to solve to brush up basics. Thanks for posting these diff Qs.
  [#permalink] 19 Aug 2004, 22:56
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A bus travelling from city A to city B breaks down midway.

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