Games
Problems
Go Pro!

Cat and Mouse Variation

Reference > Mathematics > Algebra
 

Over on the Puzzler Forum (click Puzzler Forum link at the bottom of this lesson), I posed the following riddle:

If a cat and a half can catch a mouse and a half in a day and a half, how long will it take 6 cats to catch 12 mice?

 This is a fun puzzle, and it is readily solved using the concept of direct variation and inverse variation.

The number of cats directly varies with the number of mice (in other words, if you double the number of mice, you double the number of cats and if you triple the number of mice, you triple the number of cats).

Also, the number of mice directly varies with the number of days (more mice requires more days).

Finally, the number of cats varies inversely with the number of days. If you have twice as many cats, it takes half as long to catch the mice.

So we solve this problem by holding one quantity constant while varying the other two.

We need to multiply the number of cats by 4, because there are six cats instead of 1.5. If we quadruple the number of cats, we quadruple the number of mice, so:

6 cats catch 6 mice in a day and a half.

Now we keep the number of cats constant and double the number of mice (because there are 12 instead of 6), which also doubles the number of days:

6 cats catch 12 mice in 3 days.

Now see if you can do it...

Questions

1.
If 5 boys mow 5 lawns in 5 hours, how long does it take one boy to mow 20 lawns?
2.
If 10 bees make 10 ounces of honey in 10 weeks, how many bees does it take to make 20 ounces of honey in 4 weeks?
3.
If 3 workers stack 3 cord of wood in 3 days, how many cord can 12 workers stack in 1 day?
4.
If 5 cats can catch 10 mice in 2 hours, how many hours will it take 10 cats to catch 5 mice?
5.
If a student reads a book in 5 hours, how many books can 8 students read in 1 hour?
6.
If a half a bird catches half a worm in half an hour, how long does it take 10 birds to catch 5 worms?
Assign this reference page
Click here to assign this reference page to your students.
 

Understanding Coronavirus Spread

A Question and Answer session with Professor Puzzler about the math behind infection spread.

Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources
Home
Pro Membership
About
Privacy