1 answer

A man travels 370 km partly by train and partly by car. If he covers 250 km by train and

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?

Answers

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.

.

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