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?
: It took the ant 30 seconds and the fly 15 seconds.
: Let's use a
to represent the speed of the ant,
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 ×
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.)?