A man travels 600 km partly by train and partly by car GMAT Problem Solving

Question: A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But if he travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train (T) and that of the car (C) in km/h.

       A. T = 120, C = 100
       B. T = 200, C = 180
       C. T = 60, C = 50
       D. T = 80, C = 60
       E. T = 100, C = 80

Answer: E

Approach Solution (1):
Let the speed of a train = x km/hr
And the speed of a car = y km/hr
Total distance travelled = 600km
According to the question,
If he covers 400km by train and rest by car i.e. (600 – 400) = 200km
Time take = 6hrs 30min = 6 + 30/60 = 6.5 hrs
If he travels 200km by train and rest by car i.e. (600 – 200) = 400km
He takes half hour longer i.e. 7 hours
So, total time = train time + car time
We know that,
Time = Distance /Speed
= 400/x + 200/y = 6.5 – (1)
= 200/x + 400/y = 7 – (2)
Let us take 1/x = u , 1/y = v
400u + 200v = 6.5 …(iii)
and 200u + 400v = 7 …(iv)
On multiplying Eq. (iii) by 2 and Eq. (iv) by 4, we get
800u + 400v = 13 …(a)
800u + 1600v = 28 …(b)
On subtracting Eq. (a) from Eq. (b), we get
800u + 1600v – 800u – 400v = 28 – 13
⇒1200v = 15
⇒ v= 15/1200
⇒ v = 1/80
On putting the value of v in Eq. (iv), we get
200u + 400(1/80) = 7
⇒200u + 5 = 7
⇒200u = 2
⇒ u = 1/100
So we get
u = 1/100 and v = 1/80
⇒x = 100 and y = 80
Hence, the speed of the train is 100km/hr and the speed of the car is 80km/hr
Correct option: E

Approach Solution (2):
Step 1 of 3
Given A man travels 600km partly by train and partly by car, it takes 6 hours and 30 minutes. If he travels 400km by train and the rest by car, it would take 30 minutes more if he travels 200km by train and the rest by car.
To Find: The speed of the train and car separately.

Step 2 of 3

Step 3 of 3

Correct option: E

Approach Solution (3):
Let the speed of the train be‘x’ km/hrand the speed of the car be‘y’ km/hr.
It is given that he travels400 km partly by trainand the rest i.e. (600-400) = 200 km by car
To travels this distance he takes 6 hours 30 minutes which is equal to (6 + 30/60) = 13/2 hours
Also it is given that he travels 200 km by train and the rest i.e. (600-200) = 400 km by car and the time taken is half an hour longer i.e. (13/2 + 1/2)=7 hours
Distance = Speed × Time
Now,
400/x + 200/y = 13/2→ equation 1
200/x + 400/y = 7→ equation 2
Multiplying Equation 2 with 2 we get
400/x + 800/y = 14→ equation 3
Subtracting [Equation 3] from [Equation 2] we get,
Now substituting the value of y in [Equation 2] we get
Thus the speed of the train is100 km/hr and speed of the car is 80 km/hr.
Correct option: E

“A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But if he travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train (T) and that of the car (C) in km/h.?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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