Question

A runner is jogging at a steady velocity of 3.4 km/h. When the runner is 4.1km from the finish line, a bird begins flying from the runner to the finish line at velocity 10.2km/h. When the bird reaches the finish line it turns around and flies back to the runner. Assume the birds length equals zero. How far does the bird travel?

Answer 1

Total distance covered by the bird is 6.07 km.

Explanation:

When a bird begins to fly distance of the runner from the finish line = 4.1 km

Speed of the bird = 10.2 km per hour

Therefore time taken by the bird to cover 4.1 km =
`\frac{\text{Distance}}{\text{Speed}}`

=
`(4.1)/(10.2)`

= 0.402 hours

Distance covered by the runner in 0.402 hours = Speed × time

= 3.4×0.402

= 1.3667 km

Now the distance between the bird at the finish line and the runner = 4.1 - 1.3667 = 2.6332 km

Now the runner and bird are moving towards each other.

When they meet each other they will cover the total distance of 2.6332 km in equal time.

If the bird covers the distance = x km, then the distance covered by the runner = (2.6332 - x) km

Now time taken by the bird = time taken by the runner

`(x)/(10.2)=(2.6332-x)/(3.4)`

3.4x = 26.86 - 10.2x

3.4x + 10.2x = 26.86

13.6x = 26.86

x =
`(26.86)/(13.6)`

x = 1.97 km

Total distance covered by the bird = 4.1 km + 1.97 km

= 6.07 km

Therefore, total distance covered by the bird is 6.07 km.