2 birds fly from their nest to get to a certain spot(food) in a straight line,from opposite directions (east-west) Both fly 60 km/hr.but one has a 44 km/hr tailwind to his advantage(disadvantage for the other.The bird with the advantage gets to the feeding spot 1 minute before the other. How far did the bird that got there first, travel?
To find the distance traveled by the bird that arrived first, we need to calculate the time taken by both birds. Let's assume the distance to the feeding spot is 'd' kilometers.
Let's start by calculating the time taken by the bird with the tailwind. Its effective speed is the sum of its flying speed (v) and the speed of the tailwind (w), which is 60 km/hr + 44 km/hr = 104 km/hr.
Using the formula Time = Distance / Speed, we can find the time taken by the bird with the tailwind as:
t₁ = d / 104
Now, let's calculate the time taken by the other bird, who is flying against the headwind. Since its flying speed is still 60 km/hr, we can directly use the formula:
t₂ = d / 60
Given that the bird with the tailwind arrives one minute earlier than the other bird, we know that t₂ = t₁ + 1/60.
Substituting the values of t₁ and t₂ obtained above, we get the equation:
d / 60 = d / 104 + 1/60
To solve this equation, we can eliminate the denominators by multiplying through by their common multiple (60x104):
104d = 60d + 104
Rearranging the equation, we find:
44d = 104
Dividing both sides by 44, we get:
d = 2.3636...
Therefore, the distance traveled by the bird that arrived first (and had the tailwind advantage) is approximately 2.36 kilometers.