A goods train leaves New Delhi at 5 p.m., followed by a passenger train, which leaves the station at 7 p.m. The passenger train travels 20km/hour faster than the goods train. The passenger train arrives at a station, 1040 km away, 2 hours 36 minutes before the goods train. Calculate their speeds.

Asked by Suraj | 18th Mar, 2017, 08:34: AM

Expert Answer:

begin mathsize 16px style Let space the space speed space of space the space goods space train space be space straight x space and space the space time space taken space by space it space be space straight t.
Given space that space the space passenger space train space travels space 20 space km divided by hour space faster space than space the space goods space train.
rightwards double arrow speed space of space the space passenger space train space equals space straight x plus 20 space km divided by hour

time space taken space by space the space passenger space train equals space straight t minus left parenthesis 2 space hours space 36 space minutes right parenthesis space equals space straight t minus open parentheses 2 plus 36 over 60 close parentheses equals straight t minus 2.6
Use space distance equals speed cross times time
So comma space xt equals 1040 rightwards double arrow straight t equals 1040 over straight x space.... left parenthesis straight i right parenthesis
Also comma space left parenthesis straight x plus 20 right parenthesis left parenthesis straight t minus 2.6 right parenthesis equals 1040
rightwards double arrow space left parenthesis straight x plus 20 right parenthesis open parentheses 1040 over straight x minus 2.6 close parentheses equals 1040
rightwards double arrow fraction numerator left parenthesis straight x plus 20 right parenthesis left parenthesis 1040 minus 2.6 straight x right parenthesis over denominator straight x end fraction equals 1040
1040 straight x plus 20800 minus 2.6 straight x squared minus 52 straight x equals 1040 straight x
rightwards double arrow 2.6 straight x squared plus 52 straight x minus 20800 equals 0
Dividing space throughout space by space 2.6 comma space we space get
straight x squared plus 20 straight x minus 8000 equals 0
rightwards double arrow left parenthesis straight x plus 100 right parenthesis left parenthesis straight x minus 80 right parenthesis equals 0
rightwards double arrow straight x equals negative 100 space or space straight x equals 80
So comma space the space speed space of space the space goods space train equals 80 space km divided by hr
and space the space speed space of space the space passenger space train equals straight x plus 20 equals 100 space km divided by hr end style

Answered by Rebecca Fernandes | 18th Mar, 2017, 06:23: PM

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