Question

A woman is on a lake in a rowboat located 1 mi from the closest point P of a straight shoreline (see the accompanying figure). She wishes to get to point Q, 10mi along the shore from P, by rowing to a point R between P and Q and then walking the rest of the distance. If she can row at a speed of 2mph and walk at a speed of 6 mph

how should she pick the point R (in miles from P) in order to get to Q as quickly as possible? (Round your answer to three decimal places.)

Answer 1

– 40 w – B X -R kor- Ini speed J 102 10 x att Let 'a' be the distance of a from P. so, distance. BR= 10-a. The distance traversed by her is (OR A RO). Here, OR = 2² +1² = 5x²ti Time taken to reach Ri from 0 = Jazti {os time = distan and from a to 8 = 10-2 :. Totat time to reach & from O = T= 10,*+ varu for time to be minimum, ad T =o. = te ( m + varºh y =0 => - * * * * 5 (22+5)*V2X2X=0 → ht=$3 the time į → 942 = 22+1 = x = e = are = 0.3535 20.354 PS 10. a 2 V V V 8x2=1 . For least time, the point R should distance b 1 of the point R should be at a 0.354 miles from point pi