Question 1027099
Time against wind is 800/(200-w)
Time with wind is 800/(200+w)
the units help--top is miles divided by miles/hr, so the final units are hr.
(800/(200+w))+(800/(200-w))=10
Divide everything by 10.
(80/(200+w))+(80/(200-w))=1
multiply by (200+w)(200-w)
80(200-w)+80(200+w)=40000-w^2 (internal products cancel)
32000=40,000-w^2, because the 80(-w)+80(w) cancel
w^2=8000
w=89.44 mph.
Check
on trip out, speed is 111.56 mph or 7.236 hours (here, I don't round until the end)
on way back, speed is 289.44 mph or 2.763 hours.
The exact value is 40 sqrt(5) mph