Question

On average Exante Express trains are 50km/hr faster than Paral passenger trains. A Paral passenger train requires 60% more time then Exante train to travel 1800 km from Matsay to Rawindi. Calculate average speed of each train. Calculate time it takes for each train for the journey.

Answer 1

`V- average\ speed\ of\ Exante\ Express\ train\\t-travel\ time\ of\ Exante\ Express\ train \\ \\V= (S)/(t) \ \ \ \ and\ \ \ V-50= (S)/(t+60\%t) = (S)/(1.6t)\ \ \ \ and\ \ \ S=1800\\ \\V= (1800)/(t) \ \ \ and\ \ \ V-50=(1800)/(1.6t)\ \ \ \Rightarrow\ \ \ (1800)/(t)-50= (1125)/(t) \ /\cdot t\\ \\1800-50 t=1125\ \ \ \Rightarrow\ \ \ 50t=1800-1125\ \ \ \Rightarrow\ \ \ 50t=675\ /:50\\ \\t=13.5\ [h]=13\ [h]\ 30\ [min]\\\\1.6t=21.6\ [h]=21\ [h]+ 0.6\cdot60\ [min]=21\ [h]\ 36\ [min]`


`V= (1800)/(t) =(1800)/(13,5) =133 (1)/(3) \ [km/h]\approx133.3\ [km/h]\\\\V-50\approx83.3\ [km/h]`


`Ans.\\ average\ speed\ of\ Exante\ Express\ train\ is\ 133.3\ km/h,\\travel\ time\ of\ Exante\ Express\ train\ is\ 13\ h\ 30\ min;\\average\ speed\ of\ Paral \ passenger \ train\ is\ 83.3\ km/h,\\travel\ time\ of\ Paral \ passenger\ train\ is\ 21\ h\ 36\ min`