rate × time = distance
Leg 1 r t rtLeg 2 1.5r 1.5t 2.25rtEstablish the average speed for the entire journey:Finally, focus on the exact wording of what you’re asked: the percent by which 1.3r is greater
than r. You could use the percent change formula, but no need: 1.3r is what percent greater
than 1.0r ? It is 0.3, or 30%.Picking Numbers is also a great strategy for this question. Letting r = 10 and t = 10 enables
you to slice through the intricacies of the question in seconds!8 . E
An understandable but fruitless first reaction to this question is to draw a circle and then
some triangles within it; before long, the lines become an indecipherable mass. There must
be another solution. Think a bit more abstractly about what’s happening mathematically
when you take ten points and make triangles: you’re essentially chunking a group of 10 into
subgroups of 3. Similarly, when you make heptagons in this circle, you chunk subgroups of 7
from a group of 10. So the number of triangles is
And the number of heptagons is also . No need to work out the value of this expression;
it must have a value of 120, because it’s equivalent to the expression representing the