IMAT 2015 Q6 [Cycling Journey]

Leroy cycles to work each morning. The first half of his journey is uphill and he can manage only a steady 5 kilometres per hour. The second half, however, is downhill and he covers this at 15 kilometres per hour.

Which one of these graphs could show Leroy’s journey?

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.

First, let’s eliminate some of the easy options using the information in the question. It tells us he is cycling to work, so he is going from point A to point B. Point A does not equal point B, so we can eliminate any graphs that start at 0 and finish at 0 (Why? Because 0 on the distance -y-axis is like point A. We start at this point and finish at another, resulting in a net distance travelled). So we can eliminate C and D based on this information.

Next, we need to take into consideration the distance, the point at which he changes speed (so the point at which the line changes slope), should be at the midpoint of the Y-axis. This is because it says the first HALF of his journey is at 5 km/h, and the second HALF is at 15 km/h. This means the distance is equal but the time will be different. We can eliminate any option that does not have the first half of the journey equal to the second in terms of distance. Therefore we can eliminate B.

Finally, we are left with A or E. The final choice is easy because we are left to deal with one thing: Speed. He travels the first half of the journey at a much slower rate than the second half, so the slope of the line (velocity here because velocity=distance/time) will be much steeper in the second half of the journey. Only E fits this final criterion as well as the previous ones.

\fcolorbox{red}{grey!30}{Therefore E must be the correct answer.}