Mathematics Problem Solving

Front

Jon is kayaking in the Russian River which flows downstream at a rate of 1 mile per hour. He paddles 5 miles downstream and then turns around and paddles 6 miles upstream. The trip takes 3 hours. Jon can paddle in still water at a speed of _____ miles per hour.

Back

3

Front

Andrew can paint a painting 2 times faster than Ethan can. When they work together on a painting it takes them 9 hours to paint. It would take Ethan _____ hours to paint the painting by himself.

Back

27

Front

It takes Jordan 36 minutes to mow the lawn while it takes James 45 minutes to mow the same lawn. If Jordan and James work together, using two lawn mowers, how long would it take them to mow the lawn?

Back

20

Front

The speed of a boat in still water is 30 mph. It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. The speed of the current is _____ mph.

Back

10

Front

Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours to paint a similarly-sized house. How long would it take the two painters together to paint the house?

Back

4.8

Front

Define 'Rate' in the context of problem-solving in mathematics.

Back

Rate is a ratio that compares two quantities, often expressed as a quantity per unit of time, such as miles per hour or dollars per hour.

Front

What is 'Work Rate' in mathematics?

Back

Work Rate is the amount of work done per unit of time, often used to determine how long it will take to complete a task when multiple workers are involved.

Front

Explain the concept of 'Relative Speed' in problem-solving.

Back

Relative Speed is the speed of one object as observed from another object, often used in problems involving two moving objects.

Front

What is the formula for calculating time when distance and speed are known?

Back

Time = Distance / Speed.

Front

Define 'Combined Work Rate' when two or more individuals work together.

Back

Combined Work Rate is the sum of the individual work rates of each worker, used to determine how quickly they can complete a task together.