Question
Download Solution PDFA train is moving in from north to south direction. It overtakes Raj and Madhur who are walking in the same direction at the rate of 2 km/h and 4 km/h in 9 sec and 10 sec, respectively. If the train is x metres long, find the value of x.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Speed of Raj =2 km\h
Speed of Madhur =4 km\h
Train taken to overtake Raj =9 sec
Train taken to overtake Madhur =10 sec.
Formula used:
Speed = Distance/time
km/h × 5/18=m/sec
Calculation:
When two bodies move in the same direction, then
Relative speed = Difference of their speeds
Let the length and speed of the train is x and V.
Speed of Raj is \(=2×\frac{5}{18}=\frac{5}{9}m/sec\)
Speed of Madhur
\(=4×\frac{5}{18}=\frac{10}{9}m/sec\)
Relative speed of the train and Raj
\(V-\frac{5}{9}=\frac{x}{9}\\\Rightarrow V=\frac{x}{9}+\frac{5}{9}\)
Relative speed of train and Madhur
\(V-\frac{10}{9}=\frac{x}{10}\\ \Rightarrow V=\frac{x}{10}+\frac{10}{9}\)
Now we can write
\(\frac{x}{9}+\frac{5}{9}=\frac{x}{10}+\frac{10}{9}\\\Rightarrow \frac{x}{9}-\frac{x}{10}=\frac{10}{9}-\frac{5}{9}\\\Rightarrow \frac{10x-9x}{90}=\frac{10-5}{9}\\ \Rightarrow \frac{x}{90}=\frac{5}{9}\\\Rightarrow x=\frac{5}{9}×90\\\Rightarrow x=50 m\)
Hence the length of the train is 50 m.
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