Ratios, Scales, and Unit Conversions

The video tutorial covers various mathematical problems involving ratios, rates, and scaling. It begins with calculating a cyclist's speed and time, followed by determining ingredient ratios for a sparkling grape juice recipe. The tutorial then explores scaling a circle's dimensions and comparing the cost per pound of different meats. Finally, it evaluates different map scales to fit Kansas on a page. Each section provides step-by-step solutions and explanations to enhance understanding of these mathematical concepts.

If a cyclist travels 3.75 miles in 0.3 hours, what is her speed in miles per hour?

• 15 mph

• 12.5 mph

• 10 mph

• 20 mph

How long will it take the cyclist to travel 4.5 miles at a speed of 12.5 mph?

• 21.6 minutes

• 24 minutes

• 18 minutes

• 30 minutes

To maintain the same ratio, how much sparkling water is needed for 9 quarts of grape juice?

• 15 quarts

• 21 quarts

• 12 quarts

• 18 quarts

If you have 15/4 quarts of sparkling water, how much grape juice is needed to maintain the ratio?

• 1.875 quarts

• 1.5 quarts

• 3 quarts

• 2.25 quarts

What is the area of a circle if its diameter is doubled?

• Three times the original area

• Same as the original area

• Twice the original area

• Four times the original area

Which meat is the least expensive per pound?

• Chicken

• Roast Beef

• Turkey

• Ham

Which meat is the most expensive per pound?

• Ham

• Roast Beef

• Turkey

• Pork

What scale would fit a map of Kansas on a 5x8 inch page?

• 1 in to 100 miles

• 1 cm to 1 km

• 1 in to 1 mile

• 1 cm to 200 km

If 1 inch represents 100 miles, what would be the dimensions of the map of Kansas?

• 10 in by 20 in

• 5 in by 8 in

• 15 in by 30 in

• 2.1 in by 4.1 in

Which scale is too small to fit a map of Kansas on a 5x8 inch page?

• 1 in to 100 miles

• 1 cm to 1 km

• 1 in to 10 miles

• 1 cm to 1000 km