On a track of length 100km, the train covers first 20km with a constant speed 30km/hr. What should be the speed of the train for the next 70km so that the average speed of the train remains 50km/hr for the entire trip?

1 Answer
May 8, 2018

#"157.5 km/hr"#

Explanation:

From #v = d/t# time taken to travel

  • first #20# km = #"20 km"/"30 km/hr" = 2/3\ "hr"#
  • next #70# km = #"70 km"/"v km/hr" = 70/"v"\ "hr"#

#"Average speed" = "Total distance"/"Total time"#

#"50 km/hr" = "100 km"/(2/3\ "hr" + 70/"v"\ "hr")#

#50 cancel("km/hr") = 100/(2/3 + 70/"v") cancel("km/hr")#

#50 = 100/(("2v" + 210)/("3v"))#

#50 = 100 × "3v"/("2v" + 210)#

#1/2 = "3v"/"2v + 210"#

#2 = "2v + 210"/"3v"#

#2 = 2/3 + 210/"3v"#

#4/3 = 210/"v"#

#"v = 3/4 × 210 = 157.5#