[Math] To find the total distance between two points A and B with just speed of train and difference in distance between two trains

algebra-precalculus

Two trains approach each other at 25 km/hr and 30 km/hr respectively from two points A and B. Second Train travels 20 km more than first. What is the distance between A and B ?

My approach:

Since $Distance = Speed \cdot Time$
[I just added the time it took to cover the distance taken by the Second train($30$ km/hr) to cover $20$ km to the First train($25$ km/hr) to get distance as constant]

(First Train)

For $20$ km at $25$ km/hr, the time taken would be

time $= \frac{20}{25} = \frac45$

So First train taken would take $4/5$ time more to cover the distance $d$

$d = 25 \cdot (t + 4/5 )$ —> (1)

$d = 30 \cdot t$ —> (2)

Now since distance is constant and speed is inversely proportional to time,

Ratio of speeds $= \frac{25}{30} = \frac56$

Ratio of times $ = \frac{t+4/5}{t} = \frac{\frac{5t+4}{5}}{t} = \frac{5t+4}{5t}$

So

$\frac56= \frac{5t+4}{5t}$

Since it is inversely proportional

$5(5t+4)=6(5t)$

$25t+20=30t$

$25t-30t=-20$

$-5t=-20$

$t= 4$

So applying $t=4$ in (2)
$d=30 \cdot 4 = 120$ km but its wrong

The correct answer is $220$ km

I don't understand! help

Best Answer

Let them meet after $x$ hours. We know that $25x+20=30x$, hence $x=4$. So one train travelled $25\cdot4$ km, the other $30\cdot4$ km, in total $220$ km.