Question 775819
Jane can sail upstream in a river at an average rate of 4 miles per hour, and downstream at an average rate of 6 miles per hour. If she starts at 10:00 A.M, within what period of time must she turn around if she is to return to her point of depature between 6:00 P.M and 8:00 P.M?



let the distance she has to go one way be x

time upstream = x/4

time downstream = x/6

Total time should be less than 10 hours or greater than 8 hours

8<{{{x/4 +x/6}}<10}}}

8<{{{5x/12}}<10}}}

multiply by 12

{{{96<5x<120}}}

/5
19.2 <x<24

She should return after 19.2 miles or before 24 miles

speed upstream is 4 mph

Earliest time to turn = 19.2/4 = 4.8 hours after starting ( 4 hours 48 min)

Latest time to turn 24/4 = 6 hours

She should turn after 2.48 pm

OR
She should turn before 4.00 pm



m.ananth@hotmail.ca