# $2$ tourists came from $M$ and $N$ places to meet each other at same time

$2$ tourists came at the same time from $M$ and $N$ places to meet each other, the distance between $M$ and $N$ in $33 km$. After $3$ hour and $12$ minutes distance between them reduced to $1km$, after $2$ hour and $18$ minutes First tourist's distance to cover till reaching $N$ place was $3$ times more than second tourist's distance till reaching $M$ place, find the speed of each tourist.

I've tried something like this, $v=32/3.12$ thinking it would give me average speed of both tourists then I divided it by $3$ to get the speed of first tourist but obviously got wrong numbers.

Correct answers are : $4,5km/h$ and $5,5km/h$

I've been at this problem for an hour now and still interested in how to solve this, please help.

• Just to be 100% clear, do the tourists walk in a straight line in exactly the opposite directions, or a triangle? – Tony Hellmuth Jun 18 '18 at 11:48
• should be straight line in opposite directions – JaimeLan Jun 18 '18 at 11:50
• You first talk about "the speed of each tourist", which seems to imply that there is exactly one speed per tourist, i.e., that the tourists are moving with uniform speed. But then later you talk about "average speed of both tourists", which only makes sense if their speed changes. As far as I can tell, there's no hope of solving this problem without the assumption of uniform speeds, so I suspect it's the part where you talk about the average speeds where you're mistaken. – joriki Jun 18 '18 at 11:57
• I don't know how to approach this problem anyway – JaimeLan Jun 18 '18 at 12:01

After 3 hours and 12 minutes, the total distance was reduced by $33 - 1 = 32$, which, given the speeds $v_1$ and $v_2$ for the first and second tourist respectively, tells us that:

$$v_1 + v_2 = \frac{33 - 1}{3.2} = 10 \iff v_1 = 10 - v_2$$

We also know that, 2 hours and 18 minutes later:

$$33 - (3.2 + 2.3) v_1 = 3(33 - (3.2 + 2.3)v_2) \iff v_1 = 3v_2 - 12$$

Combining both, we find:

$$10 - v_2 = 3v_2 - 12 \iff v_2 = 5.5$$

$$v_1 = 10 - v_2 = 4.5$$