Ratios, Rates, Proportional Relationships, and Units Flashcards

Two pipes together fill a tank in 6 hours. Pipe A alone fills it in 10 hours. How many hours does Pipe B alone take to fill the tank?

Answer: 15 hours

Combined rate = 1/6; Pipe A rate = 1/10; Pipe B rate = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15, so Pipe B takes 15 hours.

A car uses 6 liters of fuel per 100 km. If fuel costs $1.80 per liter, how much does it cost to drive 350 km?

Answer: $37.80

Fuel used = 350 × (6/100) = 21 liters; cost = 21 × $1.80 = $37.80.

In a poll, 3 out of every 8 people prefer brand X. If 2,400 people were polled, how many preferred brand X?

Answer: 900

3/8 × 2,400 = 900 people.

A 250 g packet of rice costs $1.50 and a 750 g packet costs $4.20. How many cents per 100 g cheaper is the larger packet?

Answer: 4 cents

250 g packet: 150/250 × 100 = 60 cents per 100 g; 750 g packet: 420/750 × 100 = 56 cents per 100 g; difference = 4 cents per 100 g.

A worker is paid $22 per hour. After taxes of 25%, what is the worker's take-home pay for a 35-hour week?

Answer: $577.50

Gross pay = 35 × $22 = $770; tax = 25% × $770 = $192.50; take-home = $770 − $192.50 = $577.50.

In a class, the ratio of students who passed to those who failed is 7:2. If 18 students failed, how many students are in the class?

Answer: 81

2 parts = 18 students, so 1 part = 9; total parts = 7 + 2 = 9; total students = 9 × 9 = 81.

Sound travels at 343 m/s. How many kilometers does sound travel in 12 minutes? (1 km = 1,000 m)

Answer: 246.96 km

Distance = 343 × (12 × 60) = 343 × 720 = 246,960 m = 246.96 km.