1. anonymous

Write a word problem describing the time it takes to complete an activity individually and with a friend. For example, if John takes 2 hours to mow his lawn and it takes his sister Maria 4 hours to mow the same lawn, how long would it take John and Maria to mow the lawn together? Write a rational equation based upon the word problem you created. The rational equation based upon the scenario above would be $\frac{ 1 }{ 2 } + \frac{ 1 }{ 4 } = \frac{ 1 }{ x }$ Each fraction represents the amount of the lawn mowed in one hour. The fraction of $\frac{ 1 }{ 2 }$ is John’s portion. Maria’s share is represented by $\frac{ 1 }{ 4 }$. The time it would take for both of them to mow the lawn is represented by $\frac{ 1 }{ x }$. Solve the rational equation. Show your work.

2. anonymous

@Hero

3. anonymous

@Aureyliant

4. Hero

Hint: $x = \dfrac{4 \times 2}{4 + 2}$

5. anonymous

ok Which part is that a hint for? the 1st part?

6. anonymous

Do you think you could help me with making a rational equation that goes with a scenario

7. anonymous

So if we say that is takes John 2 hours to paint a room and it takes Mary 3 hours to paint the same room. How long would it take for them to paint the whole room together? So would the expression be $\frac{ 1 }{ 2 } + \frac{ 1 }{ 3 } = \frac{ 1 }{ x }$ ? @Hero

8. anonymous

You're already in great hands getting help from Hero :)

9. anonymous

Ok

10. anonymous

I was just wondering because I need help solving it

11. anonymous

So would I get the LCD and solve?

12. anonymous

|dw:1434661772234:dw|

13. anonymous

|dw:1434661862797:dw|

14. anonymous

@mathstudent55

15. anonymous

@mathmate

16. anonymous

Is this right?

17. Hero

When solving a rational equation, and you need to add fractions you only need to create an LCD for the two fractions you are adding together.

18. Hero

Furthermore, including more x's in your equation is probably not a good idea.

19. anonymous

Ok so would it be |dw:1434662193097:dw|

20. Hero

The original equation you set up only had one x to begin with. You want to try to keep it that way.

21. Hero

That's much better.

22. anonymous

Ok then what do I do?

23. anonymous

Multiply by 1 to isolate x?

24. Hero

Also, here's an idea to remember about solving these. Whatever x is, it should always be less than the least time it takes one person to complete a job.

25. anonymous

Ok

26. Hero

Basically, to finish, you solve for x.

27. Hero

Isolate x.

28. anonymous

So I would do $\frac{ 5 }{ 6 } \times 1 = \frac{ 1 }{ x } \times 1 ?$

29. Hero

Ever heard of cross multiplication?

30. anonymous

Yes

31. Hero

Any time you set two fractions equal to each other, you can cross multiply as a strategy for solving for an unknown variable.

32. anonymous

so would it be |dw:1434662530398:dw|

33. anonymous

?

34. Hero

$$\dfrac{5}{6} \times \dfrac{1}{x}$$ is not the same as $$\dfrac{5}{6} = \dfrac{1}{x}$$

35. Hero

Try to avoid confusing yourself. $$\dfrac{5}{6} = \dfrac{1}{x}$$ becomes $$5x = 6$$ after cross multiplication.

36. anonymous

Ok so then I would isolate x by dividing both sides by 5?

37. Hero

Yes. And you would end up with $$x = \dfrac{6}{5}$$ but more importantly, what you want to do is convert $$\dfrac{6}{5}$$ to a mixed fraction, you'll have $$x = 1 + \dfrac{1}{5}$$ which is less than 2 (the time it takes John to complete the job) so the answer makes sense. If both John and Mary work together to complete the job, it should take less time than it would take either of them to complete the job working alone.

38. anonymous

Ok thank you so much for your help I feel like I really understood after you helped me I appreciate it a lot. Thanks so much!

39. Hero

yw