SOLUTION: flying with the wind, a bird has a speed of 90kph.but flying against the wind of only half that speed, it only made 30kph. find the speed of the wind and the bird's rate of flying

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: flying with the wind, a bird has a speed of 90kph.but flying against the wind of only half that speed, it only made 30kph. find the speed of the wind and the bird's rate of flying       Log On


   

Question 648721: flying with the wind, a bird has a speed of 90kph.but flying against the wind of only half that speed, it only made 30kph. find the speed of the wind and the bird's rate of flying when there is no wind.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = bird's speed with no wind
Let +w+ = the speed of the wind
+w%2F2+ = half of the wind speed
+b+-+w+ = bird's speed flying against the wind
+b+%2B+w+ = bird's speed flying with the wind
------------
given:
(1) +90+=+b+%2B+w+
(2) +30+=+b+-+w%2F2+
-------------------
Multiply both sides of (2) by 2
(2) +60+=+2b+-+w+
(2) +2b+-+w+=+60+
and
(1) ++b+%2B+w+=+90+
-----------------
add the equations
+3b+=+150+
+b+=+50+
and, since
(1) ++b+%2B+w+=+90+
(1) +w+=+90+-+50+
(1) +w+=+40+
The bird's speed with no wind is 50 km/hr
The speed of the wind is 40 km/hr
check:
(2) +30+=+b+-+w%2F2+
(2) +30+=+50+-+40%2F2+
(2) +30+=+50+-+20+
(2) +30+=+30+
and
(1) +90+=+b+%2B+w+
(1) +90+=+50+%2B+40+
(1) +90+=+90+
OK