Student TestMozilla Firefos iie httpswwweducosoftcomA Mrs ca

Student Test-Mozilla Firefos iie https://www.educosoft.com/A Mrs carolin rodriguez HW#1 1 :Sec 5.4: Application Part I Page 9 of 12 Total Questions:12 Score:66.666 9 10 Two cranes can unload a ship together in 8 hours. The faster crane takes 12 hours less than the slower crane, if each were to unload the same ship alonc. How long does it take for each crane to unload this ship? Solution 11 12 Faster Crane hours Slower Crane

Solution

Sol: Let x be the time of faster crane do the job alone.      x+12 be the time of faster crane do the job alone and their rates 1/x and 1/(x+12) respectively.    Rates \'x\' time=1 job done   

    (1/x+1/(x+12)).8=1

8/x+8/(x+12) =1

8(x+12)+8x=x(x+12)

8x+96+8x =x² +12x

  x² +12x-16x-96=0

  x² -4x-96 =0

  x² -12x+8x-96=0

x(x-12)+8(x-12)=0

(x-12)(x+8)=0         

   x=12 or x=-8

Take x=12 (since the rate can not be negative i.e discard x=-8)

So, faster crane =12 hours

     slower crane=24 hours