Question

A man travels 370 km partly by train and partly by car. If he covers 250 km by train and rest by car, it takes him 4 hours. But if he travels 130 km by train and the rest by car, he takes 18 mins longer. Find the speed of train and that of car?

Answer 1

Speed of train is `100` km. per hour and speed of car is `80` km. per hour.

Explanation:

Let the speed of train be `T` and that of car be `C`.

As he covers `250` km by train and rest by car i.e. `370-250=120` km. As it takes him `4` hours, we have

`250/T+120/C=4` ...................(A)

and if he travels `130` km by train and the rest i.e. `370-130=240` km by car, it takes `4` hrs. and `18` min. i.e. `43/10` hours and

`130/T+240/C=43/10` ...................(B)

Now multiplying (A) by `2` and subtracting (B) from it, we get

`(500-130)/T=8-43/10=37/10`

(note that second term on LHS cancels out)

or `370/T=37/10`

i.e. `T=(370xx10)/37=100`

Putting this in (A), we get `250/100+120/C=4`

or `5/2+120/C=4` or `120/C=4-5/2=3/2`

or `3C=120xx2=240` i.e. `C=80`

i.e. speed of train is `100` km. per hour and speed of car is `80` km. per hour.