Two bike riders, 175 miles apart, begin traveling toward each other at noon. one travels at 20 miles per hour, the other at 15 miles per hour. also at noon, a fly begins flying between the riders, starting at the front of the slower bike. the fly travels at 20 miles per hour and can change direction without losing any time. how far will the fly travel before the bicycles meet?

77

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4