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A man travels 300 kms in 13 hours, partly by rail and partly by steamer. If he had gone all the way by rail he would have ended his journey 8 hours sooner, and saved 4/5 of the time he was on steamer. How far did he go by rail?
- a)150 km
- b)130 km
- c)180 km
- d)205 km
Correct answer is option 'C'. Can you explain this answer?
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A man travels 300 kms in 13 hours, partly by rail and partly by steame...
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A man travels 300 kms in 13 hours, partly by rail and partly by steame...
Problem Analysis:
Let's assume that the distance covered by the man by rail is 'x' km and the distance covered by steamer is '300-x' km. Also, let's assume that the speed of the train is 'r' km/hour and the speed of the steamer is 's' km/hour.
Given, the total time taken by the man is 13 hours.
∴ x/r + (300-x)/s = 13 …(1)
Also, if the man had gone all the way by rail, he would have ended his journey 8 hours sooner.
∴ x/r = (300-x)/(r+s) - 8 …(2)
And, he would have saved 4/5 of the time he was on steamer.
∴ (300-x)/s - x/(r+s) = 4/5[(300-x)/s] …(3)
We have three equations (1), (2), and (3) with three variables 'x', 'r', and 's'. We need to solve these equations to find the value of 'x'.
Solution:
Let's simplify the given equations to solve for 'x'.
From equation (2), we get:
x/r + (300-x)/(r+s) = 21 …(4)
(On substituting 8 in place of (300-x)/(r+s))
From equation (3), we get:
x/(r+s) = (300-x)/(5s) …(5)
(On simplifying 4/5 of (300-x)/s)
Substituting equation (5) in equation (1), we get:
x/r + (300-x)/(r+s) = 13 - x/(r+s) …(6)
Substituting equation (4) in equation (6), we get:
21 + x/(r+s) = 13 - x/(r+s) (∵ equation (4) + equation (6))
⇒ 2x/(r+s) = -8
⇒ x/(r+s) = -4
Now, substituting x/(r+s) = -4 in equation (5), we get:
x = 180 km
Therefore, the man covered 180 km by rail.
Final Answer:
The distance covered by the man by rail is 180 km.
Let's assume that the distance covered by the man by rail is 'x' km and the distance covered by steamer is '300-x' km. Also, let's assume that the speed of the train is 'r' km/hour and the speed of the steamer is 's' km/hour.
Given, the total time taken by the man is 13 hours.
∴ x/r + (300-x)/s = 13 …(1)
Also, if the man had gone all the way by rail, he would have ended his journey 8 hours sooner.
∴ x/r = (300-x)/(r+s) - 8 …(2)
And, he would have saved 4/5 of the time he was on steamer.
∴ (300-x)/s - x/(r+s) = 4/5[(300-x)/s] …(3)
We have three equations (1), (2), and (3) with three variables 'x', 'r', and 's'. We need to solve these equations to find the value of 'x'.
Solution:
Let's simplify the given equations to solve for 'x'.
From equation (2), we get:
x/r + (300-x)/(r+s) = 21 …(4)
(On substituting 8 in place of (300-x)/(r+s))
From equation (3), we get:
x/(r+s) = (300-x)/(5s) …(5)
(On simplifying 4/5 of (300-x)/s)
Substituting equation (5) in equation (1), we get:
x/r + (300-x)/(r+s) = 13 - x/(r+s) …(6)
Substituting equation (4) in equation (6), we get:
21 + x/(r+s) = 13 - x/(r+s) (∵ equation (4) + equation (6))
⇒ 2x/(r+s) = -8
⇒ x/(r+s) = -4
Now, substituting x/(r+s) = -4 in equation (5), we get:
x = 180 km
Therefore, the man covered 180 km by rail.
Final Answer:
The distance covered by the man by rail is 180 km.
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A man travels 300 kms in 13 hours, partly by rail and partly by steamer. If he had gone all the way by rail he would have ended his journey 8 hours sooner, and saved 4/5 of the time he was on steamer. How far did he go by rail?a)150 kmb)130 km c)180 kmd)205 kmCorrect answer is option 'C'. Can you explain this answer?
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