Problem Solving

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?

(A) 1 hour
(B) 1 hour 10 minutes
(C) 2 hours 30 minutes
(D) 1 hour 40 minutes
(E) 2 hours 10 minutes

D

A |================(MEET)============================| B

Speed of A be a, Time be T1
Speed of B be b, Time be T2

Region A-MEET
A x T1 = B x (90/60)
A/B = (3/2) * (1/T1) --(1)

Region MEET-B
B x T2 = A x (40/60)
A/B = (3/2)*(T2) --(2)

equate (1) & (2)
T1*T2 = 1
Since, T1 = T2

So, T1 = 1Hr

Total time of A = T1 + 40 = 100 minutes

Answer [spoiler]{D}[/spoiler]

jose.mario.amaya wrote: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?

(A) 1 hour
(B) 1 hour 10 minutes
(C) 2 hours 30 minutes
(D) 1 hour 40 minutes
(E) 2 hours 10 minutes

D

We can plug in the answers, which represent A's total time.
When we plug in the answers:
Since A travels for 40 minutes after meeting B, the time for A and B to meet = (A's total time) - 40.
Since B travels for 90 minutes after meeting A, B's total time = (time for A and B to meet) + 90.
The answer choices imply the following times, in minutes:

A's total time = 60, time for A and B to meet = 60-40 = 20, B's total time = 20+90 = 110.
A's total time = 70, time for A and B to meet = 70-40 = 30, B's total time = 20+90 = 120.
A's total time = 150, time for A and B to meet = 150-40 = 110, B's total time = 110+90 = 200.
A's total time = 100, time for A and B to meet = 100-40 = 60, B's total time = 60+90 = 150.
A's total time = 130, time for A and B to meet = 130-40 = 90, B's total time = 90+90 = 180.

The values in red imply that we should consider a total distance that is a multiple of 7, 11 or 13 -- not likely.
Start with answer choice D, which implies a total distance that is a multiple of 100, 60, and 150 -- a far more likely scenario.

D: A's total time = 100, time for A and B to meet = 100-40 = 60, B's total time = 60+90 = 150.
Let the total distance = 300 miles.
Since A and B meet in 60 minutes, their combined rate = d/t = 300/60 = 5 miles per minute.
Since A takes 100 minutes to travel the entire distance, A's rate = d/t = 300/100 = 3 miles per minute.
Since B takes 150 minutes to travel the entire distance, B's rate = d/t = 300/150 = 2 miles per minute.
Combined rate for A and B = 3+2 = 5 miles per minute.
Success!
The values in green match.

The correct answer is D.