People who love to run love to see who can run fastest. So we have races as short as a 50-yard dash to as long as a 26-mile marathon. It takes hard work to get ready to run even a half-marathon, but a dog in Alabama ran one by accident. A bloodhound named Ludivine had stepped outside of her house, somehow found the trail for the half-marathon race that was happening, and ran the whole thing along with 165 human runners. She came in 7th place, and was the fastest “girl” runner. Ludivine did the whole race in just an hour and a half, even though she stopped to pee, sniff animals in the forest, and drink from puddles. Most of the humans couldn’t beat her even without doing those things!
Wee ones: If Ludivine finished 7th, how many runners finished before her? See if you can count them up!
Little kids: If you went running with Ludivine, how many more legs than noses would you have all together? Bonus: If she had started the race at 2:00 and ran for exactly 1 1/2 hours, when would she have finished?
Big kids: If Ludivine finished 7th out of 166 total runners, how many people finished after her? Bonus: If a marathon is 26 and 2/10ths miles long, how long is a half-marathon?
The sky’s the limit: If a bunch of humans, dogs, and squirrels all ran a race together, and there are 23 dogs and squirrels put together, 101 squirrels and people put together, and 120 people and dogs together, how many of each ran the race?
Wee ones: 6 runners (1, 2, 3, 4, 5, 6).
Little kids: 4 more, since you’d have 6 legs but just 2 noses. Bonus: At 3:30.
Big kids: 159 runners. Bonus: 13 and 1/10th miles.
The sky’s the limit: 2 squirrels, 21 dogs, and 99 people.
– If there are 23 dogs and squirrels, but 101 people and squirrels, then swapping in people for dogs raised the total by 78. There are 78 more people than dogs.
– But those two together add up to 120. That means if there were only as many people as dogs, and you didn’t add those extra 78, you’d have 42 people and dogs in equal numbers. That gives you 21 dogs.
– From there, if dogs and squirrels make 23, we have 2 squirrels. And if there are 78 more people than dogs, there are 99 people.
(Of course, you can say all of this faster with algebra:
s + d = 23, so s = 23 – d
s + p = 101
d + p = 120
Substituting for s in the second one, we get
(23 – d) + p = 101, so 23 + p = 101 + d, so p = 78 + d (take away 23 from both sides)
d + p = 120, but that p = 78 + d, so…
d + 78 + d = 120
2d + 78 = 120 (to simplify it)
2d = 42
d = 21, so there are 23 – 21 = 2 squirrels, and 21 + 78 = 99 people.)