After travelling a distance of 180 km, a train met with an accident

After travelling a distance of 180 km, a train met with an accident and then travelled at 3/4 of its original speed. It was 1 hour late in reaching its destination. If the accident had occurred a further 60 km on from the place of the accident, the delay would have been only 30 minutes. What is the total distance travelled by the train?

(A) 200 km
(B) 300 km
(C) 400 km
(D) 500 km
(E) 600 km

I used relative speeds concept.
At first calculate the difference in time taken to travel at original and reduced rates=1Hr Late - 30 Mins late = 30 Mins slower = \(1/2\) Hrs
Now frame the equation.
\(60/R\) + 1/2 = \(60/3/4R\)
\(240/3R\) - \(60/R\) =\( 1/2\)
R = 40
Rate varies inversely with time when the distance covered is the same.
a train met with an accident and then travelled at \(3/4\) of its original speed. It was 1 hour late in reaching its destination implies:
\(3/4\)th of original speed will take 4/3 times the normal time, also given \(4/3\) normal time is 1 hour late,
We can frame the equation: \(4/3T\) = T + 1 = T = 3
Distance travelled = Rate * Time = 40 * 3 = 120.
Total distance travelled = 180 + 120 = 300
B

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.