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Liz drove from point A to point B at 40 Km/h. On her way back she drov

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Bunuel
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Liz drove from point A to point B at 40 Km/h. On her way back she drov [#permalink] New post   13 Jul 2016, 02:00
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Liz drove from point A to point B at 40 Km/h. On her way back she drove at 50 Km/h and therefore her way back lasted one hour less. What is the distance (in Km) between A and B?

A. 150.
B. 200.
C. 450.
D. 500.
E. 600.
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B
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Re: Liz drove from point A to point B at 40 Km/h. On her way back she drov [#permalink] New post   13 Jul 2016, 02:38
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Bunuel wrote:
Liz drove from point A to point B at 40 Km/h. On her way back she drove at 50 Km/h and therefore her way back lasted one hour less. What is the distance (in Km) between A and B?

A. 150.
B. 200.
C. 450.
D. 500.
E. 600.


Let time by t
Therefore, 40t = 50(t-1) ( since distance = speed*time)
We get t =5
So, distance is 200 km

Another way to look at this is, she increase her speed 25% and required 1 hours less. Since distance is constant, speed and time are inversely proportional. So 1 hour reduction equates to 20 % reduction in time. 20% is 1hour so 100% is 5 hour.

20% comes by this logic - If speed increased 1/x times then time reduces by 1/(x+1) and here x = 4.
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Re: Liz drove from point A to point B at 40 Km/h. On her way back she drov [#permalink] New post   13 Jul 2016, 05:13
Bunuel wrote:
Liz drove from point A to point B at 40 Km/h. On her way back she drove at 50 Km/h and therefore her way back lasted one hour less. What is the distance (in Km) between A and B?

A. 150.
B. 200.
C. 450.
D. 500.
E. 600.


Distance is same
S1t1=s2t2
40t= 50 (t-1)
t=5

distance= speed *time
40*5= 200

B is the answer
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Re: Liz drove from point A to point B at 40 Km/h. On her way back she drov [#permalink] New post   13 Jul 2016, 06:07
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the ratio of speeds s2/s1= 50/40=5/4
since speed is inversely proportional to time
t1/t2=4/5
according to the question
1/5=1 hour
original time = 5 hours
distance = 40*5=200 km
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Liz drove from point A to point B at 40 Km/h. On her way back she drov [#permalink] New post   29 Jul 2016, 08:05
PFA. We can directly find the distance, rather than the whole way around.
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Re: Liz drove from point A to point B at 40 Km/h. On her way back she drov [#permalink] New post   31 Oct 2016, 22:11
The key is to find a find a number divisible by both 40 and 50
Only 200 fits the bill and so B is the correct answer

Alternate Solution:-
Speed from A to B * time t = Speed from B to A * time (t-1)
40 *t = 50 * (t-1)
t = 5
according to that Speed from A to B * time t = distance = 40 * 5 = 200
Correct Answer - B
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Re: Liz drove from point A to point B at 40 Km/h. On her way back she drov [#permalink] New post   01 Nov 2016, 00:47
here is my solution,

Hope it is Clear.

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Re: Liz drove from point A to point B at 40 Km/h. On her way back she drov [#permalink] New post   12 Dec 2023, 03:57
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Re: Liz drove from point A to point B at 40 Km/h. On her way back she drov [#permalink]
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