IMAT 2014 Q14 [Charity Walk]

Last month Karl walked from Starton to Endham, raising money for charity. His target, successfully achieved, was to complete the walk in ten days. He started later than intended and had only completed 12 km by the end of the first day. However, he walked 45 km on each of the second, third and fourth days, and after the fifth day he was exactly half way. Poor weather on the sixth day restricted his progress, but 41 km on both the seventh and eighth days meant that he had completed exactly three­-quarters of the walk with two days left. On the ninth day he covered three­-fifths of the remaining distance, completing the last 36 km on the tenth day.

How far did Karl walk from Starton to Endham?

A. 360 km
B. 240 km
C. 328 km
D. 384 km
E. 294 km

Here is a similar style question from the previous IMAT to practice! (IMAT 2013 Q26)

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 he completed 3/4 of the total walk on day 8. In addition, we know that there is 1/4 left to do in the last two days. We also that 2/5 of the final quarter is equal to 36 km. So first find the total of the final quarter:

Let x = amount of km in the final quarter

2x/5 = 36km
2x = 180km
x = 90km

Now we can find the amount of km in the final quarter so we can multiply it by 4 to get the total distance.

Total km = (90km)(4)
Total km = 360km

\fcolorbox{red}{grey!30}{Therefore the answer is A, $360km$.}