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Question
Hi Fredrick! So I have this summer math packet to complete before school starts, which is on August 7th. I reached a couple of problems which left me stumped because I didn't know what to do. Your help would be so appreciated. Oh, when you help me with these, would you mind telling me the process and everything? Thank you.

78. Working together, Natalie and Paul can pick forty bushels of apples in 4.8 hours. Had he done it alone, it would have taken Paul 12 hours. Find how long it would have taken Natalie.

81. An aircraft carrier left the pier traveling east eight hours before a fishing boat. The fishing boat traveled in the opposite direction for four hours, going 5 mph slower than the aircraft carrier. The ships were then 380 miles apart. What was the aircraft carrier's speed?

Answer
Here are the detailed solutions:

78. Paul's rate of picking bushels (alone) = 12 /40 = 0.3 hours per bushel

   Let Natalie's rate of picking bushels (alone) = x hours per bushel

   If their efforts were combined, then Natalie would have picked 4.8/x bushels while Paul
   would have picked 4.8/0.3 = 16 bushels in a span of 4.8 hours.

   Since 40 bushels would have been picked in a combined effort scenario,

   16 + 4.8/x = 40

   4.8/x  = 24

   x = 4.8/24 = 0.2

   Hence, if Natalie was left to pick all 40 bushels by herself, she would have taken
 
    40*0.2  = 8 hours (shown)



81. Let the aircraft carrier's speed be x mph, then the fishing boat's speed would be (x-5)

   mph.

   After the first eight hours, the aircraft carrier has traveled 8x miles and the distance
   between the two ships at this instant would simply be 8x   miles.

   In the next four hours,  the aircraft carrier would have traveled another 4x   miles
   east while the fishing boat 4(x-5) = 4x-20   miles west in the opposite direction.

   Hence, the total distance separating both ships after 12 hours would be

   8x + 4x + 4x - 20 = 16x -20

   Since this is equivalent to 380 miles,

   16x-20 = 380  =====>  x =400/16 = 25 mph (shown)



Hope this helps. Peace.  

Algebra

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Frederick Koh

Expertise

I can answer questions concerning calculus, complex numbers, vectors, statistics , algebra and trigonometry for the O level, A level and 1st/2nd year college math/engineering student.

Experience

More than 7 years of experience helping out in various homework forums. Latest presence is over at http://www.thestudentroom.co.uk/. You can also visit my main maths website http://www.whitegroupmaths.com where I have designed "question locker" vaults to store tons of fully worked math problems. A second one is currently being built. Peace.

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IEEE(Institute of Electrical and Electronics Engineers )

Education/Credentials
Former straight As A level student from HCJC (aka HCI); scored distinctions in both C and Further Mathematics B Eng (Hons) From The National University Of Singapore (NUS) B Sc (Hons) From University of London External (Grad Route)

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