SOLUTION: The tour bus has traveled the first half of your trip at only 30mph. How fast would your tour bus have to travel for the rest of your trip to have an average speed of 50mph

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: The tour bus has traveled the first half of your trip at only 30mph. How fast would your tour bus have to travel for the rest of your trip to have an average speed of 50mph      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 975007: The tour bus has traveled the first half of your trip at only 30mph. How fast would your tour bus have to travel for the rest of your trip to have an average speed of 50mph
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Very little information is given in the description. The question asks for a rate for the average rate on the trip d to be 50 mph.

RT=D, uniform rates rule for travel.


___________________speed_____________time___________distance
firsthalf__________30_________________(___)__________d/2
secndhalf__________r_________________(____)__________d/2
Totals______________________________(____)___________d

___________________speed_____________time__________________distance
firsthalf__________30________________d/(2*30)_______________d/2
secndhalf__________r_________________d/(2r)_________________d/2
Totals______________________________d(1/(2*30)+1/(2r))___________d


The time and distances sums can form the expression for average rate which must be equated to 50. distance%2Ftime:

highlight_green%28d%2F%28d%281%2F60%2B1%2F%282r%29%29%29=50%29

1%2F%281%2F60%2B1%2F%282r%29%29=50

1%2F%28r%2F%2860r%29%2B30%2F%2860r%29%29=50

1%2F%28%28r%2B30%29%2F60r%29=50

60r%2F%28r%2B30%29=50

6r%2F%28r%2B30%29=5

6r=5%28r%2B30%29

6r=5r%2B150

highlight%28r=150%29, very very fast if in mph.