A car overtakes a goods train, which is 400 m long and runni

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

A car overtakes a goods train, which is 400 m long and runni

by BTGmoderatorDC » Mon Sep 09, 2019 4:12 pm

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A car overtakes a goods train, which is 400 m long and running at 36 kph, in 8 secs. The same car crosses another goods train, which is running from opposite direction at 54 kph, in 4 secs. How long the faster train will take to cross the slower train?

A. 28 seconds
B. 2 minutes
C. 2 minutes 20 seconds
D. 3 minutes 20 seconds
E. 3 minutes 40 seconds

OA A

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Mon Sep 09, 2019 4:12 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Thu Sep 19, 2019 7:36 am

Length of the train = 400 m
Car overtakes train in 8 secs

Relative speed = $$\frac{400}{8}=50ms^{-1}$$
speed of train = 36kmph converting it to m/s
$$\frac{\left(36\cdot1000\right)}{60\cdot60}=\ 10ms^{-1}$$
$$Speed\ of\ car\ =\ Relative\ speed\ +speed\ of\ train\ =50+10=60\ \frac{m}{s}$$
The car crosses another goods train B travelling in opposite directions this time around.
Speed of time B = 54km/hr
converting it to m/s
$$\frac{\left(54\cdot1000\right)}{60\cdot60}=15ms^{-1}$$
Relative speed= Speed of car +speed of train B
= 60+15 = 75m/s
Length of train B = Relative speed * time taken = 75 *4 =300m
For the two trains given that they are travelling in opposite directions, their relative speed will be
Speed of train A + speed of train B 10 + 15 = 25 m/s
Distance = Length of the two trains = 400+300 = 700m
Time taken to cross the slower train = Distance / Relative speed
$$\frac{700}{25ms^{-1}}$$
$$=28\sec$$

$$Ans\ is\ Option\ A$$

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Sep 24, 2019 10:21 am

BTGmoderatorDC wrote:A car overtakes a goods train, which is 400 m long and running at 36 kph, in 8 secs. The same car crosses another goods train, which is running from opposite direction at 54 kph, in 4 secs. How long the faster train will take to cross the slower train?

A. 28 seconds
B. 2 minutes
C. 2 minutes 20 seconds
D. 3 minutes 20 seconds
E. 3 minutes 40 seconds

OA A

Source: e-GMAT

First, we can let r = the speed of the car (in kph) and create the equation:

8/3600 x r = 8/3600 x 36 + 400/1000

r/450 = 2/25 + 2/5

Multiplying the equation by 450, we have:

r = 36 + 180

r = 216

Next, we can let n = the length of the faster train (in meters) and create the equation:

4/3600 x 216 + 4/3600 x 54 = n/1000

6/25 + 3/50 = n/1000

Multiplying the equation by 1000, we have:

240 + 60 = n

n = 300

Finally, we can let t = the number of hours it takes the faster train to cross the slower train, and we can create the equation:

36t + 54t = 400/1000 + 300/1000

90t = 7/10

t = 7/900 hr = 28 seconds

Answer: A

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