Two trains A and B left from two stations towards station B and statio

Question

Two trains A and B left from two stations towards station B and station A respectively. 3 hours after they met, the trains were 675 miles apart. The first train arrived at its destination 16 hours after their meeting and the second train arrived at its destination 25 hours after their meeting. How long did it take for the first train to make the whole trip?

A. 18 hours
B. 36 hours
C. 25 hours
D. 48 hours
E. 60 hours

Are You Up For the Challenge: 700 Level Questions

A. 18 hours
B. 36 hours
C. 25 hours
D. 48 hours
E. 60 hours

Are You Up For the Challenge: 700 Level Questions

CosmicEnergy · Accepted Answer

There is a shortcut, meeting time = root (16*25) = 20 hours.

So, time for first train = 16 +20 = 36 hours.

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effatara · Answer

Let them meet at point M. Train A (TA) takes 16 hrs to cover MB and TB takes 25 hrs to cover MA. Let the time taken by TB to cover MB be 't' hrs which means the time taken by TA to cover AM is also 't' hrs since TA and TB both started simultaneously from A and B respectively and met at M thus covering MA and MB respectively in the same time.

Speed of TA (s1): Speed of TB (s2) = Inverse of the ratio of the times taken by TA and TB to cover MB = t/16....> s1/s2=t/16.................(i)
Similarly, s1/s2= (Time taken by TB to cover MA)/(Time taken by TA to cover MA)....> s1/s2=25/t.....................(ii)
Multiplying (i) and (ii):
(s1/s2)^2 = 25/16....> s1/s2 = 5/4
TA and TB covered 5/9 and 4/9 of the total distance (D) respectively when they met at M so TA had to cover only 4/9 of D to reach his destination B.
TA covers 4/9 of D in 16 hours so he takes (16)*(9/4)=36 hrs to cover the whole of D.
ANS:B

rsrighosh · Answer

uttamkgulshan 
This is what formula?

CosmicEnergy · Answer

There is no such formula. This is a derived shortcut after practising such questions.

Posted from my mobile device

Sabuj40040 · Answer

Sa= velocity of Train A
Sb = velocity of Train B

Gimmy · Answer

The fastest way to do this is to use logic and looking at the options available.
Since A took 16 hours to reach its destination after both trains met, and B took 25 hours to reach its destination, it means A definitely took more than 16x2=32 hours but less than 32+9=41 hours since B took 9 more hours than A to reach. Hence, the hours taken by A should be between 32 and 41 hours which is option B is the only option.

devdattakhoche · Answer

What we're solving for: 
The time it took for the first train to make the whole trip.
 Given: 
 
 After meeting, the trains were 675 miles apart in 3 hours. 
 The first train arrived at its destination 16 hours after meeting. 
 The second train arrived at its destination 25 hours after meeting.  
 
 Helpful information: 
 
 Distance = Speed × Time 
 When two objects move toward each other, their relative speed is the sum of their individual speeds.  
 
 How to solve: 
Find the speeds of the two trains and then calculate the total distance traveled by the first train. Finally, calculate the total time taken by the first train.
 
Step 1: Calculate the combined speed of the two trains
 
 The trains were 675 miles apart after 3 hours. 
 Combined speed = 675 miles / 3 hours = 225 mph  
 
Step 2: Find the ratio of the speeds of the two trains
 
 Let v1 be the speed of the first train and v2 be the speed of the second train. 
 Time taken after meeting:
 
 First train = 16 hours 
 Second train = 25 hours  
 
 The ratio of speeds is the square root of the inverse ratio of times:
 
 v1 / v2 = √(25 / 16) = 5 / 4

Step 3: Calculate individual speeds
 
 Given: v1 + v2 = 225 and v1 / v2 = 5 / 4 
 Substitute v1 = (5 / 4) × v2 into the sum:
 
 (5 / 4)v2 + v2 = 225 
 (9 / 4)v2 = 225 
 v2 = (4 / 9) × 225 = 100 mph 
 v1 = (5 / 4) × 100 = 125 mph

Step 4: Distance traveled by first train after meeting
 
 Speed of first train = 125 mph 
 Time after meeting = 16 hours 
 Distance = 125 × 16 = 2000 miles  
 
Step 5: Distance traveled by second train after meeting = distance first train covered before meeting
 
 Speed of second train = 100 mph 
 Time after meeting = 25 hours 
 Distance = 100 × 25 = 2500 miles 
 Time for first train to reach meeting point = 2500 / 125 = 20 hours  
 
Step 6: Total time taken by first train
 
 Time before meeting = 20 hours 
 Time after meeting = 16 hours 
 Total time = 20 + 16 = 36 hours  
 
✅ Final Answer: 36 hours

Vibhatu · Answer

it is very easy. see we know T=under root t1*t2; that is 20 hrs to meet . so first train complete 20 hrs +16 hours=36 hours. answer B

Kinshook · Answer

Two trains A and B left from two stations towards station B and station A respectively. 3 hours after they met, the trains were 675 miles apart. The first train arrived at its destination 16 hours after their meeting and the second train arrived at its destination 25 hours after their meeting.

How long did it take for the first train to make the whole trip?

Let distance between station A & station B be D miles and speed of train A & train B be x & y mph respectively.

Let us suppose that they met after t hours.

(x + y) t = D
x + y = D/t

(x+y)3 = 675
x + y = 675/3 = 225 mph = D/t
D = 225t miles

D/x = 16 + t ; x = D/(16+t) = 225t/(16+t) 
D/y = 25 + t ; y = D/(25+t) = 225t/(25+t)

x + y = 225 = 225t/(16+t) + 225t/(25+t) = 225t(41+2t)/(16+t)(25+t)
41t + 2t^2 = (16+t)(25+t) = 400 + 41t + t^2
t^2 = 400; t = 20 hours

Time taken by first train for the whole trip = 16 + t = 16 + 20 = 36 hours

IMO B

PietroCavallo · Answer

Here is how i did it, let me know if it makes sense:

1)  find relative speed  --> 675 (km done after meeting)/3 (hours after meeting) = 225
2)  find Individual Speeds  ---> I know A takes 16h to finish and B 25 to finish so A is 5/4 as fast as B. Therefore A/B = 5/4 & A+B = 225, in this way i know that Speed of A= 125 and Speed of B= 100
3)  use speeds to calculate total distance  ---> B takes 25 hours at 100kmh so 2500km, A takes 16 hours at 125kph so 2000km
4)  find time taken by A  ---> Tot distance= 4500/ Speed A= 125 = 36 ---->  Choice B

Saun2511 · Answer

is there a shorter quicker way to solve this @bunuel @karishmab

Adit_ · Answer

Using the shortcut t^2=root(16*25) one can solve for t=20. Then total time taken = 20+16=36.
Answer:  Option B

Two trains A and B left from two stations towards station B and statio

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Two trains A and B left from two stations towards station B and statio

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