Question : A man travels 400 km partly by train and partly by steamer. He spends 9 hours more time on the steamer. If the velocity of the steamer is 30 km/hr and the velocity of the train is 70 km/hr, how much distance does he cover by steamer?
Option 1: 309 km
Option 2: 371 km
Option 3: 464 km
Option 4: 556 km
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Correct Answer: 309 km
Solution :
Let $D$ denote the distance (in km) that the man covers by steamer.
According to the question,
$\frac{D}{30}-9=\frac{400-D}{70}$
$⇒\frac{D}{30}-9=\frac{40}{7}-\frac{D}{70}$
$⇒\frac{D}{21}=\frac{103}{7}$
$\therefore D= 309$ km
Hence, the correct answer is 309 km.
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