Question

A farmer has two tractors P and Q. Tractor P, working alone, can plough a piece of land in 5 hours while tractor Q would take 1 2/3 hours less than tractor P.

1. Determine the time the two tractors ploughing together, would take to complete the work. 
2. One day, the tractors started to plough the piece of land together. After 40 minutes, tractor P broke down but Q continued alone and completed the work.
   Calculate the total time taken to plough the piece of land that day.
3. In another season, the farmer hired an additional tractor R to assist P and Q which retained the same rate of working as before. The three tractors took 1 hour 12 minutes to plough the same piece of land. The owner of tractor R was paid some money proportional to the work done by the tractor.
   If the total work was valued at Ksh 20 000, find the amount of money paid to the owner of tractor R.    

Answer 1

1. In 1 hr P=¹/₅
   Q = ³/₁₀
   ∴ P &Q in hr → 2
                     ? → 1
        = 2 hours
2. if  1hr  → ½
     40min→?
   ⁴⁰/₆₀ x  ½ = ¹/₃ of land        
   remaining → ²/₃ of land
   1 hr Q → ³/₁₀
           ? ➛ ²/₃ 
   2 x 10 1hr
     3x3
   =2 ²/₉ hr
   total time = 2 ²/₉ hr + 40 min
   = 2hrs  53 min 20sec
   ≈ 2 hrs 53 min or 2.889 hrs
3. 1hr PQR = ⁵/ ₆  of land
                   
   1 PQ =   ½ of land              
   ∴ 1 hr R = ⁵/₆ − ½ =  ¹/₃ of land            
   1 hr R =  ¹/₃ of land
   1hr 12 min =?
   1 hr 12min  x  ¹/₃
        1 hr        
   =²/₅ of land
   amount paid =²/₅ x 20 000
                 = Ksh 8 000