# Length, Weight, and Time Problems

### Length

Units used in the USA

1 mile = 1760 yards = 5280 feet = 63,360 inches

1 yard = 3 feet = 36 inches

1 foot = 12 inches

Metric System(much more widely used around the world)

1 meter = 100 cm(centimetres)

1 kilometre = 1000 meter

As you can see the prefixes are different by a factor of 10, 100, 1000, etc. ------As shown--->

Practice Problems: Unit Conversions

1) If a man runs 3 miles, then how many yards has he run?

2) If an apple on a tree is 3 meters above the ground, how many centimetres above the ground is it?

3) If one piece of wood is 17 inches and another piece of wood is 2 yards, then what is the sum of their lengths in inches?

4) If an ant can hold something 20 times the length of it's body, how long would the longest object an ant can carry be if the ant is 0.1 decimetres (Answer is meters)?

Solutions and Explanations

1. 3 miles *1760 yards/mile = 5280 yards

2. 3 meters * 100 cm/ meter = 300 cm

3. 2 yards * 3 ft/ yard = 6 ft * 12 in/ft = 72 in

72 in +17 in = 89 in

1. 0.1 dm(decimetre) * 0.1m/dm = 0.01 meters

0.01 meters * 20 = 0.2 m

Practice Problems: Estimation

1) What US Units and Metric Units would you use to measure a someone's height?

2) if the following line was 1 yard long: _______________________________

What would be the approximate length of this line?: _________

3) What US units and Metric Units should be used to measure the length of a pencil?

1. Inches and feet, Meters and centimetres are all valid answers

2. approximately 1 foot or 0.3 yards

3. inches and centimetres

### Weight and Mass

Concept Review

Mass: The amount of space taken up by an object

Weight: The force of gravity acting upon an object

For example:

Astronauts can jump higher on the moon because gravity is weaker, so they have less weight. However, their mass remains the same.

Units of weight used in the USA

1 lb (pound) = 16 oz(ounces)

1 ton = 2000 lb

Metric System for weight(much more widely used around the world)

1 gram = 100 cg(centigrams)

1 kilogram(kg) = 1000 grams

Practice Problems: Weight

1) If a man weighs 200 lb, how many ounces does he weigh?

2) If a women can hold 100 kg, how many 100 g apples can she hold?

3) If a car can hold 1.5 tons, how many men from question 1 can theoretically sit in the car at once?

Solutions and Explanations

1. 200 lb * 16 oz/lb = 3200 oz

2. 100 kg / 100g = 100 kg / 0.1 kg = 1000 apples

3. 1.5 tons * 2000 lb / 1 ton = 3000 lb

3000 lb/200 lb = 15 men

### Time

There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute.

Example Problem:

1)If a train arrives at the station at 5:25 am comes back to the station at 1:20 pm, how long is the train gone?

5:25 am to 12:00 pm is 6 hours and 35 minutes

12:00 pm to 1:20 pm is 1 hour and 20 minutes

Therefore the total time between the trains departure and arrival is 7 hours and 55 minutes