# IMAT 2013 Q26 [Charity Walk]

Stephen is currently involved in a long distance charity walk from Alphcaster to Omegham. He left Alphcaster 9 days ago and has just completed 60% of his journey.

He hopes to complete 60% of the rest of the walk during the next 4 days. This will leave him just 60 miles from Omegham, which he aims to complete in a further 2 days.

How far is it from Alphcaster to Omegham?

A. 375 miles
B. 250 miles
C. 300 miles
D. 225 miles
E. 450 miles

Simple steps to solve word problems:

• Underline key information
• Determine what they are trying to ask, and what you will need to solve it
• Eliminate any non-essential information
• Draw a picture, graph, or equation
• In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
• Solve.

For this question, we need to work backwards. We know that 60 miles is 40% of 40%. We can make this easier by first finding the entirety of the 40% of the whole walk, so we can work all on the scale of our final answer.

To find 40% of ENTIRE walk:

60 miles = 40%

60% = 90 miles

To get that calculation easily in your head: 60 = (40)(1.5), so multiply (60 miles)(1.5).

Now we add 60 miles + 90 miles = 150 miles = 40% of entire walk.

The last steps required are basically the same idea. We have 40% of the walk and we just need to find out how much is. We can use the same method as before but note that are multiple different ways of finding the answer, you need to do what works best for you.

150 miles = 40% of total walk

(150 miles) (2.5) = 375 miles

Here, we used 2.5 because (40%)(2.5)=100%

\fcolorbox{red}{grey!30}{Therefore the answer is A, \$375\$ miles.}