Applications of equations with algebraic fractions

Lessons

1. Peter first took a train and traveled 100 km. Then, he traveled another 10 km by boat. The average speed of the train was ten times faster than the average speed of the boat; and it took Peter 11 hours to finish the whole trip.
   
   Given that the average speed of the boat was b km/h, find the average speed of the boat and complete the table below.
   

   	Distance	Speed	Time
   Train
   Boat		b

2. Two consecutive even whole numbers are selected. The difference between the reciprocal of the two numbers is $\frac{1}{144}$. Determine the numbers.
3. A rectangular cubicle in an office has an area of 81m$^2$. During a redesign of the office, the dimensions of the cubicle are altered, yet the area remains unchanged. If the width is tripled and the length is decreased by 6m, what are the dimensions of the redesigned cubicle?
4. Thomas is going on a vacation to Maui, with a flying distance of 3780 km from home. On the return flight, due to turbulence, the average flying speed was 90 km/hr slower than that of the onward flight. The time taken for the return flight was 1 hr more than for the onward flight.
   1. Calculate the average speed of the journey from home to Maui
   2. Calculate the time taken for the journey from: home to Maui
   3. Calculate the time taken for the journey from: Maui to home
5. Suppose a chef can cook for the entire restaurant in 4 hours, and his apprentice takes 12 hours. How long would it take the two of them together to cook for the restaurant?