Question

Tim was standing on a hill bird watching. He was also playing with his new stopwatch. He noticed one bird pass a certain building just when he pushed the button on his stopwatch. In one minute, the bird passed another building that Tim knew was exactly ½ mile away from the first one. How fast was that bird flying?

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Answer 1

30mph

Explanation:

We can use the concept of speed, distance, and time to solve the problem.

Let's assume that the bird was flying at a constant speed of "x" miles per minute.

When the bird passed the first building, Tim started the stopwatch. Let's say the time on the stopwatch was "t" minutes.

Therefore, the bird had flown a distance of "x*t" miles when Tim started the stopwatch.

In the next minute, the bird flew another 0.5 miles (the distance between the two buildings). So, the total distance traveled by the bird was:

x*t + 0.5 miles

We know that the total time elapsed was 1 minute. Therefore:

t + 1 = total time elapsed

Now, we can use these equations to solve for the speed of the bird:

x*t + 0.5 = distance traveled

t + 1 = total time elapsed

We want to find the value of x, so we can solve for t:

t = total time elapsed - 1

Substituting this value of t into the first equation, we get:

x*(total time elapsed - 1) + 0.5 = distance traveled

Simplifying, we get:

x*(total time elapsed) = distance traveled + 0.5

Substituting the given values, we get:

x*(1) = 0.5 + x*t

x = 0.5 + x*(total time elapsed - 1)

x = 0.5 + x*(59/60)

Solving for x, we get:

x = 30 miles per hour

Therefore, the bird was flying at a speed of 30 miles per hour.