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Hummingbird

Easy
Created: November 2, 2025

A train leaves Oakridge at 20 km/h, headed for Fairhaven. At the same time, another train leaves Fairhaven at 30 km/h, headed for Oakridge on the same track. The length of the entire track is 350 km. While this happens, a bird takes off from the front of the first train, flying alongside the track at 40 km/h. When it reaches the front of the second train, it turns around and heads back towards the first train. The bird continues this flight, going back and forth between the two trains until the two trains collide. How far would the bird have travelled by then?

Solution

280 km.

At first glance, the most straightforward way to calculate the bird’s distance travelled is to calculate the exact points in which the bird meets the front of a train and has to turn around, then add those distances up.

However, we can do better with the formula distance=speed×time\text{distance} = \text{speed} \times \text{time}distance=speed×time. We already know the speed, which leaves the time. The combined speed of both trains is 20 km/h+30 km/h=50 km/h20 \text{ km/h} + 30 \text{ km/h} = 50 \text{ km/h}20 km/h+30 km/h=50 km/h, meaning they’ll collectively cover the 350 km distance in 350 km/50 km/h=7 hours350 \text{ km} / 50 \text{ km/h} = 7 \text{ hours}350 km/50 km/h=7 hours. We substitute this into the above formula to get the total of distance=40 km/h×7 h=280 km\text{distance} = 40 \text{ km/h} \times 7 \text{ h} = 280 \text{ km}distance=40 km/h×7 h=280 km.

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