Direct and Inverse Word Problems

Front

What is a direct variation?

Back

A direct variation is a relationship between two variables in which one variable is a constant multiple of the other. If y varies directly as x, then y = kx, where k is a constant.

Front

What is an inverse variation?

Back

An inverse variation is a relationship between two variables in which the product of the two variables is a constant. If y varies inversely as x, then y = k/x, where k is a constant.

Front

If 6 men can complete a task in 15 days, how many days will it take for 5 men to complete the same task?

Back

18 days.

Front

If the speed of a plane increases, what happens to the time taken for a flight?

Back

The time taken decreases, demonstrating an inverse relationship.

Front

If a car travels 280 miles in 7 hours, how far will it travel in 12 hours?

Back

480 miles.

Front

How do you calculate the number of workers needed to complete a job faster?

Back

Use the formula: (Initial Workers * Initial Days) / New Days = New Workers.

Front

What is the formula for direct variation?

Back

y = kx, where k is a constant.

Front

What is the formula for inverse variation?

Back

y = k/x, where k is a constant.

Front

If a person weighing 90 kg has 60 kg of water, how much water is in a 75 kg person?

Back

50 kg of water.

Front

What happens to the time taken if the speed of a vehicle decreases?

Back

The time taken increases, showing an inverse relationship.