SOLUTION: A motorist travels 60 km at x km/hr and 180 km at y km/hr and takes 10 hours altogether for the journey. If the speeds are interchanged, the journey takes 8hr 40mins. Find x and y

Algebra ->  Human-and-algebraic-language -> SOLUTION: A motorist travels 60 km at x km/hr and 180 km at y km/hr and takes 10 hours altogether for the journey. If the speeds are interchanged, the journey takes 8hr 40mins. Find x and y      Log On


   

Question 1122925: A motorist travels 60 km at x km/hr and 180 km at y km/hr and takes 10 hours altogether for the journey. If the speeds are interchanged, the journey takes 8hr 40mins. Find x and y
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
system%2860%2Fx%2B180%2Fy=10%2C180%2Fx%2B60%2Fy=8%262%2F3%29

system%28X=1%2Fx%2C+Y=1%2Fy%29

Substitute the new variables.
system%2860X%2B180Y=10%2C180X%2B60Y=8%262%2F3%29

system%28180X%2B540Y=30%2C180X%2B60Y=8%262%2F3%29

480Y=21%261%2F3

Y=%2821%261%2F3%29%2F480

Back-substitute: y=480%2F21%261%2F3

highlight%28y=22%261%2F2%29------speed for second part of journey

highlight%28x=30%29-------speed for first part of journey

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A motorist travels 60 km at x km/hr and 180 km at y km/hr and takes 10 hours altogether for the journey. If the speeds are interchanged, the journey takes 8hr 40mins. Find x and y 
matrix%281%2C3%2C+60%2Fx+%2B+180%2Fy%2C+%22=%22%2C+10%29

60y + 180x = 10xy ------ Multiplying by LCD, xy ------ eq (i)





540y + 180x = 26xy ----- Multiplying by LCD, 3xy ------- eq (ii)

480y = 16xy ------------ Subtracting eq (i) from eq (ii)





matrix%281%2C3%2C+60%2F30+%2B+180%2Fy%2C+%22=%22%2C+10%29 ------ Substituting 30 for x in eq (i)

matrix%281%2C3%2C+2+%2B+180%2Fy%2C+%22=%22%2C+10%29 

2y + 180 = 10y

180 = 10y - 2y

180 = 8y