IMAT 2018 Q13 [Walking Time]

David normally takes 45 minutes to walk at a steady speed in a straight line from his house, past his friend Barry’s house and then past a shop to reach his college.

Today, however, he stopped at Barry’s house on the way and had to wait 3 minutes for him to be ready to leave. They stopped at the shop to buy their lunch, which took another 3 minutes.

It normally takes David 20 minutes to walk from his home directly to the shop and Barry normally takes 32 minutes to walk directly from his home to the college and they both walk at the same steady speed.

How long does it take them to walk from Barry’s house to the shop?

A. 7 minutes
B. 1 minute
C. 13 minutes
D. 4 minutes
E. 10 minutes

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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.

The first thing we can do is draw some timelines to show how these locations are related to each other. Note that Barry and David walk at the same speed so the velocity will be the same regardless of which one is doing the walking.

IMAT 2018 #13 no background

From this picture, we can see that we know it takes David 45 minutes to get to college and it takes Barry 32 minutes. We also know that it takes David 20 minutes to walk to Barry’s house. The easiest approach is to find out how far David is from Barry, and then we can use the known time it takes David to get to the store and subtract the distance between David and Barry, leaving just the time it takes Barry to get to the store from his house. We also know that the store is between Barry’s and the college because David passes Barry’s place before passing the shops and the college.

Distance between David’s and Barry’s = 45 minutes - 32 minutes = 13 minutes

Now we need to subtract the time it takes for David to walk to Barry’s from the time it takes David to walk to the store.

Time it takes Barry to walk to store = 20 minutes - 13 minutes = 7 minutes

\fcolorbox{red}{grey!30}{Therefore A is the answer as it would take Barry $7$ minutes to walk to the store from his house.}