A train after travelling 150 km meets with an accident and then

Question

A train after travelling 150 km meets with an accident and then proceeds at 3/5 of its former speed and arrives at its destination 8 hours late. Had the accident occurred 360 km further, it would have reached the destination 4 hours late. What is the total distance travelled by the train ?

A. 1000
B. 980
C. 840
D. 870
E. 800

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Dereno · Accepted Answer

Case 1: _ the distance between AB = 150 km, and after B he train goes at reduced speed = 3/5 s till it reaches destinationD.

Case 2 : the distance between AB = 150 km, and the point of accident accuse after 360 km. Let's consider the distance

Between B and C as 360 km.

Compare distance BC from case 1 with case 2 . Since case 1 takes t+8 hrs. And cases takes t+4 hrs.

The  difference of time b/w two cases is 4 hrs . Using speed = distance/ time formulae.

4= 360  . Solving it we get  s= 60 kmph.

Speed is reduced from S to 3/5 S the reduction is 2/5. We know that  speed is inversely proportional to time  when distance is constant.

Speed reduced by 2/5, then time increases by 2/3  . Consider case 1, the increase of time is by 8 hrs.

2/3 *t=8; hence t= 12 hrs. (Original time)

Hence, distance D = 150 + 12 (60) = 150 +720= 870 km.

ManifestDreamMBA · Answer

Let the distance covered after 150 km be d1
Given the distance covered after 150km is same, the train would have originally taken be t1 with speed s
After the accident, it took t1+8 with a speed of 3s/5
st1 = 3s/5 * (t1+8)
5t1 = 3t1+24
t1 = 12

Let the distance covered after 150+360 km be d2
Given the distance covered is same, the train would have originally taken be t2 with speed s
After the accident, it took t2+4 with a speed of 3s/5
st2 = 3s/5 * (t2+4)
5t1 = 3t1+12
t2 = 6

The train covered a distance of d2+360 in 12hours and d2 in 6hours
So, it covered 360km in 6hours, s = 60km/h

Total distance = 150+ d1 
= 150+ s*t1 
= 150 + 60*12 
= 870

ajay0520 · Answer

here we can see that it will take the train 4 hours less if the accident had happened 360 km further
which means  360/s +4 = 360/(3s/5) 
   
 considering speed of train was S and after accident the speed reduces to 3s/5
  solving this we will get s=60kmph  which is speed pf train

now using s=60 we can find  reduced speed =(3/5)*60 = 36 kmph

finally for total distance D 
we know d/60 = 150/60 + (d-150)/36 -8 (we are equating time, here the equation before = sign is time that it would take train if it traveled at normal speed of 60kmph without interruption)

solving this we will get total distance D=870

orangebicycle5 · Answer

Bunuel , can you post your official solution for this?  Dereno , has the best solution for my mind, but still struggling a bit.

My typical approach --> D=R*T,

(1) D-150 = 3/5(R) * (T+8)
(2) D - 360 = R * (T+4)

I believe the issue is on the original distance to be used, but would love to have more insight!

Yosemite98 · Answer

We know that the "delay" time will correspond to the distance traveled after the accident with a net velocity of 2/5 of original Speed.

With this in mind, for the first case:

8 hours = (D -150)/((2/5)*S)

Similarly, for the second case, 4 = (D-510)/((2/5)*S))

With simple math (getting S fromt the second equation and plugging it on the first) we get that D = 870

u2409 · Answer

d1 = remaining distance after initial speed drop point at 150km
d1 = v*t1
v = original speed
t1 = time it should take with no speed drop.
t1+8 = time it takes with speed drop

Rule: if new speed is 3/5 times the original, this means time must become 5/3 times the original to cover the same distance. 
 So, t1+8=5*t1/3 --> t1=12. So it would have taken 12 hours at normal original speed to cover d1.

d2 = remaining distance if drop point is at 510km (150km+360km)
d2 = v*t2
v = original speed
t2 = time it should take with no speed drop.
t2+4 = time it takes with speed drop
 So, t2+4=5*t1/3 --> t2=6. So it would have taken 6 hours at normal original speed to cover d2.
Now note that d1 = 360km + d2 , this means -> v*t1 = 360+v*t2 -> 12v=360+6v -> v = 60
From here d1 = t1*v = 12*60 = 720

Also note that Total distance = 150km + d1 = 150+720 = 870 km.

solankiyashx · Answer

somehow got the answer in 2 sec, dont know right apporch or not but 
 see first train travelled 150 km then met with an accident got late 8 hours.
 question says if accident happend after 360 km then train would be late by half 4 hour 
so the distance would also be double if time is double as distance and time are equally propotional
 so 360+360+150 = 870

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