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The rational expression is an expression which is expressed in the form of two integers. The rational expression is rational because one Integer is divided by the second one. Rational expression word problems is all about solving the given rational expressions. |
Example 1: Mary and Ruby are assigned a work. Mary takes 6 hours to work alone and Ruby takes 8 hours to do the same work alone. How long will it take them to complete the job if they work together?
Solution: Let t be the time taken to complete the job together.
Rate of work of Mary = $\frac{1}{6}$ per hour
Rate of work of Ruby = $\frac{1}{8}$ per hour.
If they work together time taken by them to complete the job is $\frac{1}{t}$ = $\frac{1}{6}$ + $\frac{1}{8}$
$\frac{1}{t}$ = $\frac{14}{48}$
$\therefore$ t = $\frac{24}{7}$ hrs.
Thus they both will complete the job in $\frac{24}{7}$ hours.
Example 2: Jinn and jack starts cleaning the house. Jinn cleans one third of the house within 1 hr.Jack takes same time to clean remaining part of the house. How much part of the house jack has cleaned?
Solution: Jinn cleans $\frac{1}{3}$ part of the house whereas Jack clean remaining part of the house.
The part of the house cleaned by jack is: 1 - $\frac{1}{3}$ = $\frac{2}{3}$
$\therefore$ Jack completes cleaning $\frac{2}{3}$ rd part of the house.
Example 3: Mary got a $\frac{1}{4}$ th part of water melon. She also wants share it to 3 of her friends equally. How much part of the water melon will each get including Mary?
Solution: Let the whole water melon be denoted by 1. The amount of water melon present with mary is $\frac{1}{4}$. let it be distributed to four of them which also includes mary also.
The amount of water melon each will be getting is:
$\frac{1}{4}$ $\div$ 4.
= $\frac{1}{16}$ .
$\therefore$ Each will be getting $\frac{1}{16}$ th part of the water melon.
Examples of rational expressions are: $\frac{3}{5}$, $\frac{3x}{5}$, $\frac{x + 2}{x + 3}$ etc.
For word problems with rational expressions first we have to convert the word problem into a rational expression and then we can easily solve the rational expression. Some of the solved examples of word problems with rational expressions are given below:
Example 1:
Anni and Ashley were dusting the garage. In an hour anni dusted $\frac{3}{5}$ of the garage and ashley dusted the remaining. How much portion of the garage did ashley dusted in an hour?
Portion Anni dusted in an hour = $\frac{3}{5}$
Portion Ashley dusted in an hour = 1 - $\frac{3}{5}$ = $\frac{5 - 3}{5}$ = $\frac{2}{5}$
Example 2:
The distance from Daniel's house to church is 3km. Daniel walks at the speed of $\frac{1km}{20min}$ from his house to church. The church service is for an hour and while returning home from church he walks at the speed of $\frac{1km}{25min}$. How much time does it take for Daniel to reach his house if he leaves the house at 8AM for the service?
Time taken from house to church = $\frac{20}{1}$ x 3 = 60 minutes
Time taken in the service = 1 hour = 60 minutes
Time taken from church to house = $\frac{25}{1}$ x 3 = 75 minutes
Total time taken = 60 + 60 + 75 = 195 minutes = 3hr15min
It takes 3$\frac{1}{4}$hr for Daniel to reach house once he leaves for church. So Daniel reaches the house at 11:15AM.