SOLUTION: A plane can travel 910 miles with a 35 mph tailwind in the same time it can travel 760 miles with 49mph headwind. How fast can the plane travel with no wind resistance?

Question 524123: A plane can travel 910 miles with a 35 mph tailwind in the same time it can travel 760 miles with 49mph headwind. How fast can the plane travel with no wind resistance?
Found 2 solutions by mananth, oberobic:
Answer by mananth(16949) (Show Source): You can put this solution on YOUR website!
plane speed x mph
Tail wind 35 mph
Head wind = 49
..
against wind x - 49 mph
with wind x + 35 mph

Distance against wind 760
Distance with wind 910
Time = same
760 /(x- 49 )= 910 /(x+ 35 )
760 *(x+ 35 )= 910 *(x- 49 )
760 x + 37240 = 910 x -44590
910 x -760 x = 44590 + 37240
150 x = 81830
/ 150
x= 545.53 mph

Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The basic distance equation is d=r*t
.
910 = (s+35) * t, where s = indicated airspeed of the plane and t = time
.
760 = (s-49) * t
.
We are told t=t
.
t = 910/(s+35)
and
t = 760(/(s-49)
.
910/(s+35) = 760/(s-49)
.
cross multiply
.
910*(s-49) = 760*(s+35)
.
910s - 44590 = 760s + 26600
.
150s = 26600 + 44590 = 71190
.
s = 71190/150
.
s = 474.6 mph
.
Check the times to be sure this answer is correct.
.
t = 910/(s+35)
t = 910/(474.6+35)
t = 1.785714285714286
.
t = 760(/(474.6-49)
t = 1.785714285714286
.
Correct.
.
Answer: With no wind resistance (or assistance) the airplane can fly 474.6 mph.
.
Done.
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