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 solve this problem, we need to break it down into smaller steps. Let's proceed step by step:
Step 1: Understand the given information.
- We have two birds flying towards a certain spot (food) in a straight line.
- They are flying from opposite directions - one from the east and one from the west.
- Both birds are flying at a speed of 60 km/hr.
- One of the birds has a tailwind of 44 km/hr, giving it an advantage.
- The bird with the advantage arrives at the feeding spot 1 minute before the other bird.
Step 2: Define the variables.
Let's assume that the distance both birds travel to reach the feeding spot is "D" km.
Step 3: Understand the concept of relative speed.
When two objects are moving towards each other, their relative speed is the sum of their individual speeds. Similarly, when two objects are moving away from each other, their relative speed is the difference between their individual speeds.
Step 4: Calculate the relative speed.
Since both birds are flying towards each other, their relative speed is the sum of their speeds: 60 km/hr + 60 km/hr = 120 km/hr.
Step 5: Determine the time difference.
We know that one bird arrives one minute before the other. This means that the total travel time for the bird with the advantage is one minute less than the total travel time for the other bird.
Step 6: Apply the concept of time, speed, and distance.
The formula to calculate time is:
Time = Distance / Speed
For the bird with the advantage (tailwind):
Time = D / (60 + 44) [since its speed is 60 km/hr and it has a tailwind of 44 km/hr]
For the other bird:
Time = D / (60 - 44) [since its speed is 60 km/hr and it has a headwind of 44 km/hr]
The time difference is given as 1 minute, which can be converted to hours (1/60 hours).
Therefore, we can set up the equation: (D / (60 + 44)) - (D / (60 - 44)) = 1/60
Step 7: Solve the equation.
To calculate the distance traveled by the bird with the advantage (D), we solve the equation.
[(D / 104) - (D / 16)] = 1/60
Simplify and solve for D.
(15D - 98D) = 104
-83D = 104
D = -104 / 83
Therefore, the distance traveled by the bird that arrived first is approximately 1.25 km (rounded to two decimal places).
Hence, the bird that got there first traveled approximately 1.25 km.