Ratios, Rates, Proportional Relationships, and Units Flashcards

A container that holds 5 gallons is 40% full. How many more gallons must be added to make it 90% full?

Answer: 2.5 gallons

Current = 0.40 × 5 = 2 gal; target = 0.90 × 5 = 4.5 gal; add 4.5 − 2 = 2.5 gallons.

A jogger runs at 7.5 mph. A cyclist rides 3 times as fast. How many miles can the cyclist travel in 40 minutes?

Answer: 15 miles

Cyclist speed = 3 × 7.5 = 22.5 mph; distance in 40 min = 22.5 × (40/60) = 22.5 × 2/3 = 15 miles.

The lengths of the sides of a rectangle are in the ratio 5:8. If the perimeter is 104 cm, what is the area of the rectangle?

Answer: 640 cm²

2(5k + 8k) = 26k = 104, so k = 4; sides = 20 cm and 32 cm; area = 20 × 32 = 640 cm².

A photograph 4 in × 5 in is enlarged proportionally so the longer side becomes 20 in. What is the length of the shorter side?

Answer: 16 inches

Scale factor = 20 ÷ 5 = 4; shorter side = 4 × 4 = 16 inches.

A 180-gram snack package is 45% carbohydrates. If the serving size is 30 grams, how many grams of carbohydrates are in one serving?

Answer: 13.5 grams

45% of 30 grams = 0.45 × 30 = 13.5 grams.

A hiker descends a 900-meter trail in 1.5 hours, then climbs back up at half the descent speed. How long does the round trip take?

Answer: 4.5 hours

Descent rate = 900 ÷ 1.5 = 600 m/hr; ascent rate = 300 m/hr; ascent time = 900 ÷ 300 = 3 hours; total = 1.5 + 3 = 4.5 hours.

In a school election, Candidate A received 60% of the votes and Candidate B received the rest. If B got 240 votes, how many students voted in total?

Answer: 600 students

B got 40% of votes; 240 = 0.40 × total; total = 240 ÷ 0.40 = 600 students.