SIMPLIFYING RATIONAL EXPRESSIONS WORD PROBLEMS

Problem 1 :

Pari needs 4 hours to complete a work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together?

Solution :

Number of hours taken by pari  =  4 hours

Number of hours taken by Yuvan  =  6 hours

Work done in one hour by Pari  =  1/4

Work done in one hour by Pari  =  1/6

work done by together in one hour  =  (1/4) + (1/6)

  =  (6 + 4)/4(6)

  =  10 / 24

  =  5/12

Number of hours taken by both  =  12/5

Let us convert into minutes  =  (12/5) 60  =  144 minutes

  =  2 hours 24 minutes.

Problem 2 :

Iniya bought 50 kg of fruits consisting of apples and bananas. She paid twice as much per kg for the apple as she did for the banana. If Iniya bought ₹ 1800 worth of apples and ₹ 600 worth bananas, then how many kgs of each fruit did she buy?

Solution :

Let "x" be number of kgs of banana and "2x" be the number of kgs of apple.

Cost of apple  =  1800

Number of kgs of apple (cost per kg)  =  1800

Number of kgs of apple (2x)  =  1800

Number of kgs of apple  =  1800/2x  =  900/x  -----(1)

Number of kgs of banana (cost per kg)  =  600

Number of kgs of banana (x)  =  600

Number of kgs of apple  =  600/x  -----(2)

(1) + (2)

(900/x) + (600/x)  =  50

(1500 / x)  =  50

x  =  1500/50

x  =  30

By applying x = 30 in (1), we get 

  Number of kgs of apple  =  1800/2(30)  =  30

By applying x = 30 in (2), we get 

  Number of kgs of banana  =  600/30  =  20

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