Ratios, Rates, Proportional Relationships, and Units Flashcards

Two cars start at the same point and drive in opposite directions. Car A travels at 55 mph and Car B at 45 mph. After how many hours are they 300 miles apart?

Answer: 3 hours

Combined separation rate = 55 + 45 = 100 mph; time = 300 ÷ 100 = 3 hours.

A $200 item is marked down by 20%, then the sale price is increased by 20%. What is the final price?

Answer: $192

Sale price = $200 × 0.80 = $160; final = $160 × 1.20 = $192.

A tank initially contains 120 liters. Water flows in at 8 L/min and drains at 5 L/min. How many minutes until the tank holds 195 liters?

Answer: 25 minutes

Net fill rate = 8 − 5 = 3 L/min; needed = 195 − 120 = 75 liters; time = 75 ÷ 3 = 25 minutes.

A runner completes 3/5 of a marathon (26.2 miles) in 2 hours. At this pace, what is her predicted finishing time in hours?

Answer: 3 hr 20 min

Full race time = 2 ÷ (3/5) = 2 × 5/3 = 10/3 hours = 3 hours 20 minutes.

A square tile has a side length of 30 cm. How many tiles are needed to cover a floor that is 6 m × 4.5 m? (1 m = 100 cm)

Answer: 300

Floor area = 600 × 450 = 270,000 cm²; tile area = 30² = 900 cm²; tiles = 270,000 ÷ 900 = 300.

The rate of interest on a savings account is 4% per year simple interest. If $2,500 is deposited for 3 years, what is the total amount in the account?

Answer: $2,800

Interest = 2,500 × 0.04 × 3 = $300; total = $2,500 + $300 = $2,800.

A 120-meter long train passes a stationary signal pole in 8 seconds. What is the speed of the train in km/h?

Answer: 54 km/h

Speed = 120/8 = 15 m/s; in km/h: 15 × 3600/1000 = 54 km/h.