The average speed of a high-speed train in japan in 162 miles per hour. at this rate how many miles would the high-speed train travel in 45 minutes.

a.40.5 miles
b.72.9 miles
c.81.0 miles
d.121.5 miles

the answer is d. because if you know how to turn hours into minutes then you would figure it out

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