SOLUTION: A train, an hour after starting, meets an accident which detains it one hour, after which it proceed at 3/5 of its former rate and arrives 3 hours late. But, had accident happened

Question 30584: A train, an hour after starting, meets an accident which detains it one hour, after which it proceed at 3/5 of its former rate and arrives 3 hours late. But, had accident happened 80km farther, it would have been 1.5 hours late only. Find the original rate of the train and the length of the journey.
Answer by Fermat(136) (Show Source): You can put this solution on YOUR website!
Let v1 be the speed before the breakdown
Let v2 be the speed after the breakdown
v2 = (3/5)v1
============
The two journeys are identical except for the 80km part
let s1 be the distance up to the 80 km part
The difference in time taken between travelling the 80 km at v1 and at v2 is equal to the difference in time of the two late journeys - which difference is 1.5 hrs.
In other words, it takes 1.5 hrs longer to travel 80 km when trvelling at v2 than it does when travelling at v1.
time to travel 80 km at v1 = 80/v1 = t1
time to travel 80 km at v2 = 80/v2 = t2
t2 - t1 = 1.5
80/v2 - 80/v1 = 3/2
80(1/v2 - 1/v1) = 3/2
(80/v1)(5/3 - 1) = 3/2
(80/v1)(2/3) = 3/2
80/v1 = 9/4
v1 = 320/9
v1 = 35.5556 km/hr
==================
Let s2 be the distance travelled after the breakdown (in the first joiuurney), such that,
s1 + s2 = L, where L is the overall journey distance travelled from the start to the final destination.
Let T be the journey time without breakdowns.
L = v1T
=======
In the first journey, excluding the 1hrs wait time, it takes 2hrs longer to travel the distance s2, at the speed v2, than at the speed v1 (normal/standard speed)
t = s2/v1
t' = s2/v2
t' - t = 2
s2(1/v2 - 1/v1) = 2
(s2/v1)(5/3 - 1) = 2
s2/v1 = 2*3/2 = 3
s2 = 3v1
s2 = 106.6667 km
================
The distance s1 is travelled in 1 hr (given) at speed v1
s1 = 35.5556*1
s1 = 35.5556 km
===============
L = s1 + s2
L = 35.5556 + 106.6667
L = 142.2222 km
===============
RELATED QUESTIONS
a train, an hour after starting, meets with an accident which detains it an hour .after... (answered by ankor@dixie-net.com)

A train, an hour after starting, meets with an accident which detains it an hour, after... (answered by ankor@dixie-net.com)

A train travelling from Ay town to Bee town meets with an accident after 1 hour. The... (answered by josmiceli)

A train running from A to B meets with an accident 50 miles from A, after which it... (answered by ankor@dixie-net.com)

A train after traveling 150 km meets with an accident and then proceeds with 3/5 of its... (answered by ankor@dixie-net.com)

Hi A train after travelling 50km meets an accident and and after reducing 3/4 of its... (answered by mananth,ikleyn)

A battleship started at 7:00 AM on a 500 mile voyage on a special mission but was brought (answered by ankor@dixie-net.com)

A train traveling from Avondale to Bimmaeus stops at a cracked rail after 1 hour, and the (answered by ikleyn,Edwin McCravy,mccravyedwin)

1) Two trains X and Y enter at the same time a tunnel 1 Km. long at the opposite ends.... (answered by ankor@dixie-net.com)