Word Problems Simplifying Rational Expressions :
Here we are going to see some word problems on simplifying rational expressions.
Question 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?
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
Number of hours taken by both = 12/5
Let us convert into minutes = (12/5) 60 = 144 minutes
= 2 hours 24 minutes.
Question 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?
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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