Nash is training for a marathon and decides to train for 26 miles every week. In the first week, the ratio of the number of miles he ran to the number of miles he walked was 3:10. Use Scratchpad to draw tape diagrams to represent this ratio. How many miles did Nash run in week 11?

-1/2 +2

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