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Back to the Ski Slopes


Yes, we are back on the mountain and trying to work out the speed of our skiers. We remember (from a Math lesson a long time ago) that Speed = Distance/Time. It was given to us in a triangle, something like this:

To use this triangle, simply put your finger over the letter you are solving for.

If you want to know S for Speed, then putting your finger over S gives D/T (distance divided by time). If you want to solve for D then covering it up you have S · T or Speed x Time.

So, out skier covers 10kms in 45min. We want to work out her speed in kms per hour, so we first have to make sure that we are dividing by hours. 45 min = 45/60 hours or 3/4 hours (three quarters of an hour). So our speed is now = 10kms/0.75hrs which equals 13.33kms. Now, she might have stopped off for hot chocolate at the warming hut and actually done a much faster speed while travelling. But that’s another math problem for another day!


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10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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