Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The problem statement:

Distance between two stations A and B is 230 km. Two motorcyclist starts simultaneously from A and B in opposite directions and the distance between them after 4 hours is 50 kms. Speed of each of them in km/hr is:

$$ (a) 40, 30 \quad \quad (b)27, 17 \quad \quad (c) 50,40 \quad \quad (d)None $$

The suggested answer is (a) and in the solution it is stated that "Total distance covered here is $280$ kms $(230+50)$ and not $180$ kms $(230-50)$".

But I am not getting this reasoning, could somebody explain me why are we adding instead of subtracting?

share|improve this question
add comment

1 Answer 1

up vote 2 down vote accepted

There are two cases: either they haven't met - or they have met. If they haven't the total distance is $230-50 = 180$ and hence the sum of speed is $45$. No answer fits. While if we assume that they have met on their path - then they done these $50$km after they met - so we add them to $230$km they have done before they met and obtain $280$. As a result, the sum of speeds is $70$ - and we have an answer (a) which fits this result.

The case that they were going in the opposite directions, but not from $A$ to $B$ and from $B$ to $A$ cannot happen since after some time the distance has decreased. While it could happen on a sufficiently small sphere, though - it's unlikely that it was meant in this problem.

share|improve this answer
1  
This was my reasoning when I first attempt the problem, but the problem setters (seem to) have a different point of view. –  Quixotic Feb 22 '12 at 16:06
    
@Foool: Since you've posted your comment before I've put the whole version of the answer, I am not sure if your comment still applies. –  Ilya Feb 22 '12 at 16:07
    
Well, given the "None" as one of the option, this seems to be a very tricky problem that requires a student to take care of both cases before he/she chooses an option. –  Quixotic Feb 22 '12 at 16:20
1  
@Foool Think of $\begin{align} 4v_1+4v_2 &= 230 \pm 50\\ (v_1+v_2) &= 57.5 \pm 12.5\\ &= 70 \vee 45 \end{align}$ –  user13838 Feb 23 '12 at 12:08
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.