"3 out of 4" Questions - Rate and Proportion

Look or sound familiar? 



"A 10 metre flag pole casts a shadow of 6 metres. A 12 metre pole would cast a shadow that is ______ metres in length."

"A motorcyclist rides 125 miles in 3 hours. At this rate, how much distance will be covered in 5 hours?"

A factory produces 3000 widgets every 45 minutes. How many widgets will be produced in 7 hours?


These questions, I like to call, are "3 out of 4" questions. You are given 3 numbers and you need to find the 4th. How to solve? Make yourself a 4-way relationship box. 


Let's look at question 1 again. 

"A 10 metre flag pole casts a shadow of 6 metres. A 12 metre pole would cast a shadow that is ______ metres in length."

Your two "measurements" are height (H) and shadow length (SL).

H           SL
10            6
12            ?

Remember MUADO - Multiply Up and Across, Divide by the Other Number.

12 x 6 = 72
72/10 = 7.2

You could have set your box up another way.

H      10    12
SL     6      ?

6 x 12 = 72
72/10 = 7.2

Same answer...


Tricks to watch out for!

In question 3, the two "measurements" are time and widgets. However, the first "time" is in minutes and the second one is in hours. You need to either convert the 45 minutes to .75 hours, or convert the 7 hours to 420 minutes. Then set up your box, remember MUADO, and get yourself the right answer.

Solving Triangle Questions That Don't Really Look Like Triangle Questions

The GED exam may well have one word question involving a hiker, a boat or an airplane travelling so far in one direction, turning then travelling so far in a second direction.


There may also be a question with a grid, where you are asked to find the distance between two given points.

Believe it or not, these are triangle questions.

Example. A hiker walks 3 km due south, then turns and walks 4 km due east. How far is the hiker from the starting point? (The boat and airplane questions are similarly worded.) You might be tempted to answer "7", which would be incorrect.

How to solve? Draw a picture. Of a right-angled triangle.

You now have a Pythagorean question, where you have the two short legs and you are looking for the hypotenuse (long side.) You may also recognise this as a 3/4/5 triangle, where the hypotenuse is 5. There's your answer - 5.