Mark has two pets, a hare that runs 10 feet/second and a turtle that crawls 1 foot/second. If they're going to run a 20 foot-race, how much of a head start (in seconds) does the turtle need to finish in a tie? Give the rationale and then the answer.
Let's think step by step. We can find how long the hare spends running by dividing the distance of the race by the hare's speed: 20 feet / 10 feet / second = 2 seconds. We can do the same for the turtle: 20 feet / 1 foot / second = 20 seconds. Finally, subtract the hare's run time from the turtle's run time to find the length of the head start the turtle needs: 20 seconds - 2 seconds = 18 seconds.. The answer is: 18.

The PTA had saved $400 set aside after a fundraising event. They spent a fourth of the money on school supplies. Then they spent half of what was left on food for the faculty. How much money did they have left? Give the rationale and then the answer.
Let's think step by step. They spent $400 / 4 = $100 on school supplies. They spent $300 / 2 = $150 on food. They had $300 - 150 = $150 left.. The answer is: 150.

A group of 300 athletes spent Saturday night at Ultimate Fitness Camp. The next morning, for 4 hours straight, they left the camp at a rate of 28 athletes per hour. Over the next 7 hours, a new group of athletes trickled into the camp at a rate of 15 athletes per hour. Immediately thereafter, the camp gate was shut and everyone went to bed. What is the difference in the total number of athletes in the camp over the two nights? Give the rationale and then the answer.
Let's think step by step. The number that left the camp on Saturday morning was 4 * 28 = 112 athletes. This means that in the camp there remained 300 - 112 = 188 athletes. The new group trickling in on Sunday morning comprised 7 * 15 = 105 athletes. The number that slept at the camp on Sunday night is therefore 188 + 105 = 293 athletes. Since there were 300 athletes on Saturday night, the difference is 300 - 293 = 7 athletes.. The answer is: 7.