IMAT 2017 Q9 [Distance as a Function of Time]

The distance from Ardale to Banby is 16 km and from Banby to Carston is a further 8 km in the same direction.

David leaves Ardale at 11.00 and runs for an hour at 6 km / h. He rests for 20 minutes and then completes the rest of the distance to Banby at an average speed of 10 km / h. He chats with some friends in Banby for 20 minutes and then borrows a bicycle from one of them and cycles to Carston at an average speed of 16 km / h. David leaves Carston at 15.00 and cycles back over his route, arriving home at 15.50.

Which one of the following correctly shows David’s distance from Ardale as a function of time?



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, we need to realize that the X-axis is time, and the Y-axis is distance from the start point (this is because it will end at 0 when he goes back home).

We will solve this by taking key information and then eliminating any answer choice that does not meet it.

Starting with the slopes, we know that the first part is done at 6km/h, the second part is done at 10km/h, the third part at 16km/h, and we do not know the last part. We can find the last part by taking the distance from Ardale to Banby + the distance from Banby to Carston, and then dividing this by the 50 minutes it takes to get home. However, we do not even need to calculate this and you will see why.

Based on the speeds in the first three parts, the sequence should be: Slope 1 < Slope 2 < Slope 3, Why? Because he is progressively getting faster and so the line should get steeper. This piece of information can help us eliminate B and D.

Next, we are told that the first two breaks are both 20 minutes each, so the first two plateaus in the graph should be the same length. This eliminates C because the second break is longer than the first in it. Now we are left with A and E.

We can immediately rule out E because the slope of the final way back home is vertical, which is logically impossible. We know you must cover 16km + 8km in 50 min, which will not result in a 0 slope.

\fcolorbox{red}{grey!30}{Therefore A is the correct answer}
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