A person travels 340 km in 8 h. The first part of the journey, he travels by car at the speed of 50 km/h and in the second part of the journey he travels by train at the speed of 38 km/h. How many km did he travel by train?a)120 kmb)190 kmc)150 kmd)210 kmCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Average speed of the journey = 340/8 km/h

By the rule of Allegation :

Time spent in car : Time spent in train = 9/2 : 15/2 = 3 : 5

Time spent in train = 5/8 x 8 = 5 h

Distance travelled by train = 38 x 5 = 190 km

Answer

To solve this problem, we can use the formula:

Distance = Speed × Time

First, let's find the time taken for the first part of the journey by car. Let's assume the distance covered by car is 'x' km.

So, according to the given information, the speed of the car is 50 km/h and the time taken is 8 hours.

Since Distance = Speed × Time, we can write the equation as:

x = 50 × t1

where t1 is the time taken for the first part of the journey.

Rearranging the equation, we get:

t1 = x / 50

Next, let's find the time taken for the second part of the journey by train. The total distance covered is 340 km, and the distance covered by car is 'x' km. So, the distance covered by train is (340 - x) km.

The speed of the train is 38 km/h, and the time taken is also 8 hours.

Using the formula Distance = Speed × Time, we can write the equation as:

(340 - x) = 38 × t2

where t2 is the time taken for the second part of the journey.

Rearranging the equation, we get:

t2 = (340 - x) / 38

Since the total time taken for the journey is 8 hours, we can write the equation:

t1 + t2 = 8

Substituting the values of t1 and t2 from the above equations, we get:

x / 50 + (340 - x) / 38 = 8

Now, we can solve this equation to find the value of x, which represents the distance covered by car.

By solving the equation, we get:

(38x + 50(340 - x)) / (50 × 38) = 8

Simplifying further, we get:

38x + 17000 - 50x = 15200

-12x = -1800

x = 150

Therefore, the distance covered by train is 340 - 150 = 190 km.

Hence, the correct answer is option B) 190 km.

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