SOLUTION: Ramesh and Narendra start from the same place and arrive at another place in 40 minutes and 60 minutes respectively. If Narendra starts 10 minute earlier than Ramesh, how much ti

Let our clock/chronometer starts (t=0) at the moment When Narendra starts.


    Let D be the distance between the starting and ending points.

    Then  the Ramesh    rate of move is    linear units per minute, 
    while the Narendra  rate of move is   linear units per minute.


The equation for Narendra position is  = ,       0 <= t <=60

The equation for Ramesh   position is  = ,  10 <= t <= 40.

The time moment when Ramesh will take to reach Narendra is determined from the equation  

 = ,    or

 = .


To solve it, first cancel D in both side, and then multiply both sides by 240. You will get an equivalent equation

4t = 6*(t-10)  ====>  4t = 6t - 60  ====>  2t = 60  ====>  t =  = 30.


Answer.  Ramesh will take Narendra in 30 minutes after Narendra started, or in 30-10 = 20 minutes after Ramesh started.

Let distance traveled to "another place," be D

Then Ramesh’s speed = , or 

Also, Narendra’s speed = , or D



Let time it takes Ramesh to reach Narendra (get to catch-up point), be T

Then Narendra’s time to get to catch-up point = , or 

We then get the following DISTANCE equation: 



9DT = 6DT + D -------- Multiplying by LCD, 6

9DT – 6DT = D

3DT = D

T, or time Ramesh takes to catch up to Narendra, if Narendra leaves 10 minutes before Ramesh = 

****Note: You failed to mention that when they left the SAME PLACE, they did so at the SAME TIME.

So, it should be:: Ramesh and Narendra start from the same place AT THE SAME TIME and arrive at another place in 40 minutes and 60 minutes respectively.



I don't have to, because I already read it.  English is my 1st language and I've been learning, speaking, and writing it for 30+ years now. I do understand 

English quite well, and for the most part am able to understand, decipher, and sometimes even correct others on math problems. I did the problem the way I 

understand it, and unless someone can prove to me that I misinterpreted the question that was asked, I stand by my answer, 100%.



Yes, Narendra starts 10 minutes before Ramesh, and gets to the catch up point in 30 minutes, while Ramesh takes 20 (30 - 10) minutes to get to the catch-point. 

What I'll do is use REAL numbers to illustrate this!



Let Narendra's speed be 50 kmh

Then Ramesh's is 1.5(50), or 75 kmh (Ramesh speed is  of Narendra's)

In 60 minutes, or 1 hour Narendra completed the trip, and so the distance = 50(1), or 50 km

In 40 minutes, or , or  hr, Ramesh completed  = 50 km

Note that that was what was given (The faster Ramesh completed the trip, in 20 minutes less time than Narendra)

This makes sense, since Narendra CAN NEVER catch-up with Ramesh when they leave at the same time. But, if Narendra leaves 10 minutes before Ramesh, then they will meet at some point.



Now, 10 minutes after leaving, Narendra will have traveled: 

At this time, Ramesh leaves, and Narendra will be  km ahead of Ramesh

Therefore, 20 minutes after this, Narendra will have traveled another: 

Therefore Narendra will have traveled a total of: 

In the meantime, during the 20 minutes that have elapsed since Ramesh left, Ramesh will have covered 

As seen, 30 minutes after Narendra left, she covered 25 km, and 20 minutes after Ramesh left, he also covered 25 km. The 25 km is the catch-up point.