Christian Brothers School 2007 Prelim
Question:
There were 2 identical flights of steps. For the 1st flight of steps, James walked up some steps and ran 6 steps in 74s. For the 2nd flight of steps, James walked up some steps and ran 14 steps in 42s. How long will James take to walk up both flights of steps?


Do you find this question challenging? Well, I do.

This question actually appeared in year 2005 PSLE Math examination, if I recalled the year correctly.

In fact, ever since that year, many schools used this question either as work practices or as exam questions. Despite the fact that the students were taught the strategy to solve this question, I noticed many still do not understand the logics behind the solution and therefore, are still unable to solve it.


The following is my step-by-step solution.


First, let me show you the 2 identical flights of steps.












If James ran 6 steps and walked the rest of the steps, he will take 74 seconds.












If James ran 14 steps and walked the rest of the steps, he will take 42 seconds.












By comparing the two flights of steps below, I can logically say that the difference in time for James to walk up the 2 flights of steps is caused by walking up the 8 steps in the first flight instead of running up the 8 steps in the second flight.












If James took 32 seconds (74sec – 42sec) more to walk up 8 steps instead of to run up 8 steps, therefore, the extra time needed to walk up 1 step as compared to run up 1 step is 4 seconds longer. (Logic & Reasoning: Walking time is normally longer than running time)












To calculate the time taken to walk up the entire flight of steps, I will just need to convert the time to “run 6 steps” to walking:

If James needs 4 seconds more to walk up 1 step than to run up 1 step, therefore, he will need 24 seconds (6 steps x 4 seonds) more to walk up 6 steps than to run up 6 steps.












So, if James were to walk up the entire flight of steps, he will take 98 seconds (74 + 24).











If I calculate the time for James to walk up the second flight of steps, I should obtain the same time as the first flight of steps, that is 98 seconds.

Well, to prove it, let's work out the workings:

If James needs 4 seconds more to walk up 1 step than to run up 1 step, he will need 56 seconds (14 steps x 4 seconds) more to walk up 14 steps than to run up 14 steps.










Therefore, if James walks up the entire flight of steps, he will also take 98 seconds (42 + 56)!

Therefore to answer the question,
For James to walk up the two flights of steps, he will take 196 seconds (98 + 98).












Did my drawings help you visualize the question and solution better?

For you to master solving this question, my advice is that you should practice this question at least once after watching the solution.

Then, solve this question again 2 days later, but without watching the solution.

If you are able to do it, congratulations! …. because you have truly understood the logics of solving it!!

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Bye,
Norman Tien
http://www.pslemath.com/