Problem Solving

Q: Two ICE Express Trains started simultaneously from L.A for Las-Vegas , which are 390 km apart. The ratio of speed of the two trains is 6 : 7 . After travelling how long (in kms ) should the trains exchange their speed so that both the trains reach their destination at the same time ( simultaneously ).

a) 150 km

b) 190 km

c) 210 km

d) 250 km

e) 290 km

OA[spoiler]C)[/spoiler]

Let's call the time the two trains moved with their original speeds is t1, and the time after they switched their speeds is t2

For train 1 ( speed 6x) :
6x*t1 + 7x*t2 = 390

For train 2 (speed 7x):
7x*t1 + 6x*t2 = 390

Then 6x*t1 + 7x*t2 = 7x*t1 + 6x*t2
or x*t2 = x*t1 (deduct both equations to 6x*t1+6x*t2)
Hence t1 = t2, or 13x*t1 =390
Then at the time the two trains switched their speeds, train 1 had moved 6*t1/13*t1 = 6/3 the way
Train 2 had moved 7*t1/13*t1 = 7/13 the way
So after t1, the two trains are at:
train 1: 6/13 * 390 = 180km
train 2: 7/13*390 = 210km
So pick C.

Hi Aman,

There are two trains A and B.
The length of the route is 390 km.
The ratio of speed of the two trains is 6 : 7.
Therefore, the trains A and B should exchange their speeds after travelling 6/(6+7)*390 km and 7/(6+7)*390 km, respectively. The answer should be either 180 km or 210 km.
Correct answer is C.

Hope it helps!
Best,
Maciek