After covering a distance of 30km. With a uniform speed there is some defect in a train enzine and therefore its speed is reduced to 4/5 of its original speed consiquetely the train reaches its destination late by 45 minutes had it happened after covering 18 km. More the train would have reached 9 minutes earlier find the speed of train and distance of journey

Asked by Ankujsingla | 26th Sep, 2018, 01:32: PM

Expert Answer:

Let,
the speed of the train = x km/hr
the total distance covered by the train = y km
begin mathsize 16px style rightwards double arrow Original space time space taken space to space reach space the space destination space equals space straight y over straight x hrs
Reduced space speed space of space the space train space equals space fraction numerator 4 straight x over denominator 5 end fraction km divided by hr
end style
According to the first  condition, we get
 
Time taken at original speed + time taken at reduced speed = original time taken + 45 minutes
begin mathsize 16px style rightwards double arrow 30 over straight x plus space fraction numerator left parenthesis straight y minus 30 right parenthesis over denominator open parentheses begin display style 4 over 5 end style straight x close parentheses end fraction equals space straight y over straight x plus space 45 over 60
after space solving comma space we space get
rightwards double arrow straight y space minus space 3 straight x space equals space 30 space space space space............ left parenthesis straight i right parenthesis end style
 
According to the second condition, we get
begin mathsize 16px style rightwards double arrow 48 over straight x plus fraction numerator left parenthesis straight y space minus space 48 right parenthesis over denominator open parentheses begin display style 4 over 5 end style straight x close parentheses end fraction space equals space straight y over straight x space plus space 36 space
After space solving comma space we space get
5 straight y space minus space 12 straight x space equals space 240 space..... left parenthesis ii right parenthesis

Solve space equation left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space simultaneously comma space we space get
straight x space equals space 30 space and space straight y space equals space 120
Therefore space the space original space speed space of space the space train space equals space 30 space km divided by hr space and space the space length space of space the space journey space equals space 120 km end style
 
 

Answered by Yasmeen Khan | 27th Sep, 2018, 12:52: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.