SOLUTION: Rashi travels 300km to her home partly by train and partly by bus. She takes 4 hours to travel 60km by train and the remaining by bus. If she travels 100km by train and the remaini

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Rashi travels 300km to her home partly by train and partly by bus. She takes 4 hours to travel 60km by train and the remaining by bus. If she travels 100km by train and the remaini      Log On


   

Question 925194: Rashi travels 300km to her home partly by train and partly by bus. She takes 4 hours to travel 60km by train and the remaining by bus. If she travels 100km by train and the remaining by bus she takes 10 minutes longer. . Find the speed of train and bus separately.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in hrs she spent traveling
by bus in the 1st case
+300+-+60+=+240+ km = distance in km traveled
by bus in the 1st case
---------------------
The speed of the bus is:
+240+%2F+t+ km/hr
The speed of the train is:
+60%2F4+=+15+ km/hr
---------------------
In the 2nd case:
+d%2Fr%5B1%5D+%2B+d%2Fr%5B2%5D+ = total time of travel
+100%2F15+%2B+%28+300+-+100+%29+%2F+%28%28+240%2Ft+%29%29+=+4+%2B+t+%2B+10%2F60+
+20%2F3+%2B+200%2A%28+t%2F240+%29+=+25%2F6+%2B+t+
+40%2F6+%2B+%285%2F6%29%2At+=+25%2F6+%2B+%286%2F6%29%2At+
+40+%2B+5t+=+25+%2B+6t+
+t+=+15+ hrs
---------------
The speed of the bus is:
+240%2Ft+=+240%2F15+
+240%2Ft+=+16+ km/hr
--------------------
The speed of the train is:
+60%2F4+=+15+ km/hr
-----------------------
check answer:
+100%2F15+%2B+%28+300+-+100+%29+%2F+%28%28+240%2Ft+%29%29+=+4+%2B+t+%2B+10%2F60+
+100%2F15+%2B+200+%2F+%28%28+240%2F15+%29%29+=+4+%2B+15+%2B+1%2F6+
+20%2F3+%2B+200+%2F+16+=+19+%2B+1%2F6+
+6+%2B+2%2F3+%2B+25%2F2+=+19+%2B+1%2F6+
+13+=+12.5+%2B+4%2F6+-+1%2F6+
+13+=+13+
OK