$2$ 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.
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:
$$10 - v_2 = 3v_2 - 12 \iff v_2 = 5.5$$
$$v_1 = 10 - v_2 = 4.5$$