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Natansha
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A and B start from Opladen and Cologne respectively at the 06 Sep 2025, 07:12
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Got this as you have equated the ratios of speed so it makes sense now. However I saw a post above which said,

''When two elements travel at different speeds, their TIME RATIO to travel the same distance will always be the same.'' and they have equated the time ratios, can we do that and what will be the logic behind that?

KarishmaB


This is what is given:

The distance from Opladen to M, A takes t mins and B takes 90 mins to cover. So their speeds are in the ratio 90 : t (same distance so ratio of speeds is inverse of ratio of time taken)
The distance from M to Cologne, A takes 40 mins and B takes t mins to cover. So their speeds are also in the ratio t : 40 (same distance so ratio of speeds is inverse of ratio of time taken)

Of course both are the ratio of their speeds A: B so both are the same ratio.
Hence

\(\frac{90}{t} = \frac{t}{40}\)

which means t = 60 mins

So A took 1 hour and 40 mins to cover the distance from Opladen to Cologne.

Answer (D)
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Kinshook
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A and B start from Opladen and Cologne respectively at the 06 Sep 2025, 08:00
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A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 90 minutes after their meeting.

How long did A take to cover the distance between Opladen and Cologne?

Let the distance between Opladen and Cologne be D km and speed of A & B be vA & vB km/hours respectively

Let they meet after time t hours

Distance travelled by A = vA*t km
Distance travelled by B = vB*t km
vA*t + vB*t = D
vA+vB = D/t

vB*t = vA*40/60 = 2vA/3
vA/vB = 3t/2
vA*t = vB*90/60 = 3vB/2
vA/vB = 3/2t = 3t/2
t = 1 hour
They meet after 1 hour

A take to cover the distance between Opladen and Cologne = 1 hour + 40 minutes

IMO D
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