HCHS

PROBLEMS OF THE WEEK

2003-2004

TANK PROBLEM : One pipe can fill a tank in 15 minutes, another pipe can fill it in 20 minutes, a third pipe 30 minutes. With all three pipes open, how long will it take to fill the empty tank?

CHICKEN MCNUGGET PROBLEM : McDonald's sells chicken mcnuggets in boxes of 6, 9, and 20.

1. Is it possible to get exactly 17 mcnuggets? If yes, what is the combination?

2. Can you get exactly 53 mcnuggets? If yes, what is the combination?

3. What is the largest number of mcnuggets that is impossible to get exactly? Show your work.

4. If the boxes were 7, 11, and 17, what is the largest number of mcnuggets that is impossible to get exactly? Show your work.

BIG TIRES : An automobile was fitted at the factory with 30 inch diameter tires. That means its speedometer is calibrated for 30 inch diameter tires. If you replace all the tires with 31 inch diameter tires, how will this effect the speedometer readings? 1. If you drive with the speedometer at 55 mph, how fast are you actually going? 2. At what speed would you have to drive to actually travel at 55 mph?

SQUARE PROBLEM : The figure below is a rectangle with a rectangular hole. The sides of the outer rectangular boundary measures 9 cm by 12 cm. The inner rectangular measures 1 cm by 8 cm. Cut this figure along two paths that, fitted together, form a complete square.

Extra Credit: Solve the problem above. Turn in all work with the solution. Please try to do your own work. If you work with someone else, please let me know. No work will be accepted once the solution is posted on this website. Occasionally, hints will be provided. Use these only if you need them. Keep checking back since hints could be posted anytime during the week.