SOLUTION: A plane can travel 910 miles with a 35 mph tailwind in the same time it can travel 760 miles with a 40 mph headwind. How fast can the plane travel with no wind resistance?

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A plane can travel 910 miles with a 35 mph tailwind in the same time it can travel 760 miles with a 40 mph headwind. How fast can the plane travel with no wind resistance?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 769242: A plane can travel 910 miles with a 35 mph tailwind in the same time it can travel 760 miles with a 40 mph headwind. How fast can the plane travel with no wind resistance?
Answer by josgarithmetic(39800) About Me  (Show Source):
You can put this solution on YOUR website!
Basic concept is r*t=d, r rate, t time, d distance.
Including tailwind help, rate is r+35.
Including headwind hindrance, rate is r-40.

910 mph with tailwind, time t, distance unknown.
r%2B35=910%2Ft
760 mph with headwind, time t, distance unknown.
r-40=760%2Ft
Those two equations just use the meaning of rate for traveling or motion. MILES per TIME.

"in the same time..." The value for t is the same number in both equations.
t%28r%2B35%29=910
t=910%2F%28r%2B35%29
and
t%28r-40%29=760
t=760%2F%28r-40%29

EQUATE the expressions for t:
highlight%28910%2F%28r%2B35%29=760%2F%28r-40%29%29
SOLVE FOR r.