Racing Cars on Figure-8 Track

Five racing cars are tearing along on a figure-8 track that has a total length of 7 miles. The cars A, B, C, D, and E have speeds, respectively, of 60, 72, 75, 80, and 96 mph. High walls are located along each side of the track; and so, should any two cars meet at the center, they will collide. Each driver is wondering, “How did I get myself into this? Who is Stella?” If the cars started at the center, all going the same way, will two cars eventually collide? If so, which two, and after how many miles and how many minutes?

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Grapefruit Stack (14)

On a special day at the West Side Market, the grapefruit are arranged in a compact stack of filled-in equilateral triangles with 14 grapefruit on each edge of the bottom triangle, 13 on each edge of the one above, and so on all the way up to the top where there is 1 graperfruit sitting all alone. How many grapefruit are in the entire stack?

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Babysitting Formula

Liz earned d dollars for h hours of babysitting. At that rate, how much will she earn in x hours? Write a formula that works. Then use numbers to check it: Make up a reasonable hourly rate for babysitting, assume she sits for 3 hours (that’s h), and get her total (that’s d). Now figure out what she’d get for 5 hours (that’s x) and see if your formula works.

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