Rational Expressions Word Problems

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.
We can solve the Rational expressions in the following types:
Direct problems:
$\frac{5}{4}$ + $\frac{3}{7}$
$\frac{7}{3}$ - $\frac{2}{6}$
$\frac{4}{5}$ $\times$ $\frac{6}{4}$
$\frac{7}{2}$ $\div$ $\frac{6}{5}$.
We solve these problems directly by performing the operations.

Solving the equations which are of the form of function:
eg: f₁(x) = x² + 3x + 2 and f₂ (x) = x + 2.
In these kind of problems, we have to solve for x.
 

Rational Expressions Applications Word Problems

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.

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.


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.