Ratios and Proportions Flashcards

A hoisting system has a mechanical advantage ratio of 3:1. If a worker applies 90 pounds of force, what maximum load can be lifted?

Answer: 270 pounds

A 3:1 mechanical advantage means the output force is 3 times the input force. 90 × 3 = 270 pounds. This ratio tells you how many times the system multiplies your effort.

A blueprint uses a 1:50 scale. A shaft measures 8 centimeters on the blueprint. What is the actual shaft length in meters?

Answer: 4 m

Scale 1:50 means every 1 cm on paper = 50 cm in reality. 8 cm × 50 = 400 cm = 4 meters. Convert centimeters to meters by dividing by 100.

A drive gear turns at 180 RPM and is connected to a driven gear with a gear ratio of 6:1. What is the speed of the driven gear?

Answer: 30 RPM

A gear ratio of 6:1 means the driving gear turns 6 times for every 1 turn of the driven gear. 180 ÷ 6 = 30 RPM. A higher ratio reduces the output speed.

Concrete mix requires cement, sand, and gravel in the ratio 1:2:4. If a job needs 28 bags of gravel, how many bags of cement are required?

Answer: 7 bags

In a 1:2:4 ratio, for every 4 parts gravel there is 1 part cement. 28 ÷ 4 = 7. Cement bags = (1/4) × 28 = 7 bags.

A pump fills a tank at a rate of 45 gallons every 3 minutes. At the same rate, how many gallons will it pump in 11 minutes?

Answer: 165 gallons

The unit rate is 45 ÷ 3 = 15 gallons per minute. 15 × 11 = 165 gallons. Set up the proportion: 45/3 = x/11, then cross-multiply.

A job requires mixing two lubricants in a 5:3 ratio by volume. If the total mixture needed is 40 liters, how many liters of the first lubricant are required?

Answer: 25 liters

The total ratio parts are 5 + 3 = 8 parts. The first lubricant is 5 out of 8 parts. (5/8) × 40 = 25 liters.