time speed dist

mitaliisrani wrote:A man covered a distance of 200 kms partly by train and partly by bus. Had he covered the entire distance by bus, he would have taken 10 hours more and had he covered the entire distance by train, he would have taken 6 hours less. What was the difference between the distances (in kms) covered by him by bus and train?

a)60 b)75 c)50 d)90

OA is B

If the difference between the distances (in km) covered by him by bus and train is x, and if we are free to take for granted more distance covered by train than by the bus and that the train being faster than the bus, then distance covered by train is ½ (200 + x) and distance covered by bus is ½ (200 - x). Furthermore, if b is bus speed and t is train speed, then total time taken was

½ (200 + x)/t + ½ (200 - x)/b.

Since bus takes 10 more hours to cover ½ (200 + x) than the train does, hence

½ (200 + x)/b – ½ (200 + x)/t = 10

Or (1/b – 1/t) = 20/ (200 + x).

And, since bus takes 6 more hours to cover ½ (200 – x) than the train does, hence

½ (200 - x)/b – ½ (200 - x)/t = 6

Or (1/b – 1/t) = 12/ (200 - x).

Equating, we get

20/ (200 + x) = 12/ (200 - x); solving gets me [spoiler]50[/spoiler], BUT

Please check the OA and cite the source

When I tried this, I got 3 variables and 2 equations, so it was unsolvable by me.

I would love to know how to solve this.

kmittal82 wrote:When I tried this, I got 3 variables and 2 equations, so it was unsolvable by me.

I would love to know how to solve this.

Please help me help you out

sanju09 wrote:

kmittal82 wrote:When I tried this, I got 3 variables and 2 equations, so it was unsolvable by me.

I would love to know how to solve this.

Please help me help you out

Let x be the distance travelled by bus
200 - x is the distance travelled by train

Let b be the speed of the bus
Let t be the speed of the train

total time taken to cover the distance = x/b + 200-x/t

So, from the question we know:
>Had he covered the entire distance by bus, he would have taken 10 hours more

Time taken to cover whole distance by bus = 200/b

=> 200/b = x/b + (200-x)/t + 10

>and had he covered the entire distance by train he would have taken 6 hours less

Time taken to cover the distance by train = 200/t

=> 200/t = x/b + (200-x)/t - 6

We need to find x, and we now have 3 unknowns -> t, b and x, but only 2 equations

It is important to assign the right variable(s) in complex situations as this one. Safest is to assign x to the question in chief, as I did above. I too used 3 variables but the purpose was crystal clear, to get the final equation in x alone.