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Speed is distance covered divided by time, while velocity is displacement divided by time. Velocity is a vector quantity while speed is not. An example of when speed would be decreasing yet velocity would be increasing occurs when a car driving in reverse slows down. If it was going 30m/s and then slowed town to 10m/s, the speed would be slowing down. However, since the car is moving along the negative x axis, its initial velocity vector would be -30m/s and it would decellerate to a velocity of -10m/s.

The example isn't great, but you can get the picture that the way that this is possible is by the fact that speed is a scalar quantity while velocity is vector.

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