# For Geeks & Brainiacs #06- Trading Places -

An ant is on one side of a branch and a fly is on the other side of the branch.

For a change of scenery, they decide to swap places. So the ant crawls along the branch from A to B and
the fly crawls along the branch from B to A. They each travel in a perfectly horizontal line. After they
pass each other, it takes the ant 20 seconds to reach point B, while it takes the fly only 5 seconds
to reach point A. How much time did it take each insect to make the journey?

**HINT**:

*Distance = Speed x Time*. Use algebra to represent the time each insect travels before and
after they meet.

**ANSWER**:

*It took the ant 30 seconds and the fly 15 seconds.*
**EXPLANATION**: Let's use

**a** to represent the speed of the ant,

**f** to represent the
speed of the fly, and

**t** to represent the number of seconds it takes for them to cross paths. Use
the formula

*Distance = Speed x Time* to obtain the distance covered by each insect before and after
they meet. The ant travels

**a** ×

**t** before meeting and

**a** ×

**20** after
meeting. The fly travels

**f** ×

**t** before meeting and

**f** ×

**5** after
meeting. The distance traveled by the ant before the insects meet is equal to the distance traveled by the
fly after the insects meet (and vice versa). So

**a** ×

**t** =

**f** ×

**5**
and

**f** ×

**t** =

**a** ×

**20**. With two simultaneous equations, you can
solve for t = 10 (the number of seconds it takes the insects to cross paths). Therefore the ant requires
10 + 20 = 30 seconds to make the trip, and the fly requires 10 + 5 = 15 seconds.

Do you have a

suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?