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Manasvi1
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A man travels 600 km partly by train and partly by car 27 May 2020, 02:05
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35% (medium)

Question Stats:

75% (02:38) correct 25% (03:04) wrong based on 177 sessions

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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
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E
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nick1816
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A man travels 600 km partly by train and partly by car 27 May 2020, 21:39
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\(\frac{200}{c} - \frac{200}{t} = 0.5\) .....(1)

\(\frac{400}{t}+\frac{200}{c }= 6.5 \).....(2)

Subtract (1) from (2)

\(\frac{600}{t}= 6\)

t = 100

E




Manasvi1
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
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A man travels 600 km partly by train and partly by car 28 May 2020, 01:54
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nick1816
\(\frac{200}{c} - \frac{200}{t} = 0.5\) .....(1)

\(\frac{400}{t}+\frac{200}{c }= 6.5 \).....(2)

Subtract (1) from (2)

\(\frac{600}{t}= 6\)

t = 100

E




Manasvi1
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


Could you please explain how equation 1 is derived
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A man travels 600 km partly by train and partly by car 28 May 2020, 02:34
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Manasvi1
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

Amazing approach nick1816

I have learned this approach from nick1816 only.

The man lost 30 minutes when he traveled 200 kms by train and 400 kms by car.
If he had traveled 400 kms instead of 200 kms by train he could have saved 30 minutes means he lost time when he traveled that extra 200 kms with car(more time)
Time= Distance/ Speed
Lost time= [200/(speed of car)]-200/(speed of Train)
30/60=(200/C)-(200/T)
next equation
(400/T)+(200/C)=13/2(6 hrs 30 minutes)
From both the equation
400/T+200/T=(13-1)/2
600/T=6
T=100
E:)
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A man travels 600 km partly by train and partly by car 28 May 2020, 10:25
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satya2029 explained it perfectly.

A.............B.............C............D

Suppose AD=600 Kms. Divide AD in 3 equal parts. AB=BC=CD=200 Kms

Case 1 - He travels distance AB by a train, distance BC by a train and distance CD by a car

Case 2- He travels distance AB by a train, distance BC by a car and distance CD bya car.

We can clearly see that he gonna take equal time to travel Distance AB and Distance CD in both cases, as he's using the same mean. So definitely gonna take extra time in case 2 while travelling Distance BC.

Hence, \(\frac{BC}{c} - \frac{BC}{t} = 0.5\) or \(\frac{200}{c} - \frac{200}{t} =0.5\)


sume3tss
nick1816
\(\frac{200}{c} - \frac{200}{t} = 0.5\) .....(1)

\(\frac{400}{t}+\frac{200}{c }= 6.5 \).....(2)

Subtract (1) from (2)

\(\frac{600}{t}= 6\)

t = 100

E




Manasvi1
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


Could you please explain how equation 1 is derived
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A man travels 600 km partly by train and partly by car 01 Jun 2020, 08:02
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Manasvi1
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

We can create the equations:

400/T + 200/C = 6.5

and

200/T + 400/C = 7

Multiplying the first equation by 2, we have:

800/T + 400/C = 13

Subtracting the second equation from the equation above, we have:

600/T = 6

T = 100

We see that only choice E has T = 100; therefore, it must be the correct answer.

Answer: E
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A man travels 600 km partly by train and partly by car 07 Jun 2020, 00:46
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Hello!

I followed a quick approach which helped me save a lot of time by not doing the equations.
In the 1st case,
Distance travelled by Train is 400 kms and by Car is 200 kms, which takes 6.5 hrs
Speed=Distance/Time
So, 600/6.5= 92.30 kms/hr

In the 2nd case,
Distance travelled by Train is 200 kms and by Car is 600 kms, which takes 7 hrs
Speed=Distance/Time
So, 600/7= 85.7 kms/hr

Considering the options given,
Add speeds from Case 1 and Case 2,
92.30+85.70= 178

178/2= 89kms/hr

89kms/hr is closest to Option E in terms of getting an average.

Official Answer-: Option E

Regards,
Raunak Damle :thumbsup:
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A man travels 600 km partly by train and partly by car 30 Dec 2024, 05:33
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Hello from the GMAT Club BumpBot!

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