Question : A man travels 450 km to his home, partly by train and partly by car. It takes 8 hours and 40 minutes if he travels 240 km by train and rests by car. It takes 20 minutes more if he travels 180 km by train and the rest by car. The speed of the car in km/h is:
Option 1: 45
Option 2: 50
Option 3: 60
Option 4: 48
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Correct Answer: 45
Solution :
Let the speed of the train and the car be $a$ km/h and $b$ km/h, respectively.
According to the question,
$\frac{240}{a}+\frac{450–240}{b}=8\frac{40}{60}$
⇒ $\frac{240}{a}+\frac{210}{b}=\frac{26}{3}$ ---------------------------(equation 1)
Also, $\frac{180}{a}+\frac{450–180}{b}=9$
⇒ $\frac{180}{a}+\frac{270}{b}=9$ --------------------------------------(equation 2)
Multiply equation 1 by 3 and equation 2 by 4 we get,
$\frac{720}{a}+\frac{630}{b}=26$ --------------------------------------(equation 3)
$\frac{720}{a}+\frac{1080}{b}=36$ ------------------------------------(equation 4)
Now subtracting equation 3 from equation 4 we get,
⇒ $\frac{450}{b}=10$
⇒ $b=45$ km/h
Hence, the correct answer is 45.
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