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06 Sep 2025, 07:12
Kudos
Bookmarks
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?
''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
06 Sep 2025, 08:00
Kudos
Bookmarks
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
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
17 May 2026, 00:21
Kudos
Bookmarks
Let:
* A’s speed = a
* B’s speed = b
They start at same time and meet after t minutes.
STEP 1: Distances before meeting
Before meeting:
A travels:
at
B travels:
bt
STEP 2: Use the “swapped remaining distances” idea
After meeting:
* A still has to travel the part B already covered before meeting.
* B still has to travel the part A already covered before meeting.
So:
A after meeting:
A takes 40 min after meeting.
Distance traveled by A after meeting:
40a
But this equals B’s pre-meeting distance:
bt
So:
40a = bt
B after meeting:
B takes 90 min after meeting.
Distance traveled by B after meeting:
90b
But this equals A’s pre-meeting distance:
at
So:
90b = at
Now we have:
40a = bt
90b = at
STEP 3: Find speed ratio
Divide the two equations:
40a / 90b = bt / at
Simplify right side:
bt / at = b / a
So:
40a / 90b = b / a
Simplify left side:
4a / 9b = b / a
Cross multiply:
4a2 = 9b2
Take square root:
a / b = 3 / 2
So:
A speed : B speed = 3 : 2
STEP 4: Use speed ratio to get meeting time
Since speeds are 3 : 2,
before meeting their distances are also 3 : 2
(because they traveled for same time before meeting).
Suppose:
a = 3k
b = 2k
Using:
40a = bt
Substitute:
40(3k) = 2k(t)
120k = 2kt
Cancel 2k:
t = 60
So they met after 60 minutes.
STEP 5: Find A’s total travel time
A traveled:
* 60 min before meeting
* 40 min after meeting
Total:
60 + 40 = 100 minutes
= 1 hour 40 minutes
Answer: D
* A’s speed = a
* B’s speed = b
They start at same time and meet after t minutes.
STEP 1: Distances before meeting
Before meeting:
A travels:
at
B travels:
bt
STEP 2: Use the “swapped remaining distances” idea
After meeting:
* A still has to travel the part B already covered before meeting.
* B still has to travel the part A already covered before meeting.
So:
A after meeting:
A takes 40 min after meeting.
Distance traveled by A after meeting:
40a
But this equals B’s pre-meeting distance:
bt
So:
40a = bt
B after meeting:
B takes 90 min after meeting.
Distance traveled by B after meeting:
90b
But this equals A’s pre-meeting distance:
at
So:
90b = at
Now we have:
40a = bt
90b = at
STEP 3: Find speed ratio
Divide the two equations:
40a / 90b = bt / at
Simplify right side:
bt / at = b / a
So:
40a / 90b = b / a
Simplify left side:
4a / 9b = b / a
Cross multiply:
4a2 = 9b2
Take square root:
a / b = 3 / 2
So:
A speed : B speed = 3 : 2
STEP 4: Use speed ratio to get meeting time
Since speeds are 3 : 2,
before meeting their distances are also 3 : 2
(because they traveled for same time before meeting).
Suppose:
a = 3k
b = 2k
Using:
40a = bt
Substitute:
40(3k) = 2k(t)
120k = 2kt
Cancel 2k:
t = 60
So they met after 60 minutes.
STEP 5: Find A’s total travel time
A traveled:
* 60 min before meeting
* 40 min after meeting
Total:
60 + 40 = 100 minutes
= 1 hour 40 minutes
Answer: D
