Question

Solve the rational equation, Medal will be given

1/40 + 1/25 = 1/x

Eric and Lance both play a video game, It takes Eric 40 minutes to beat the round. But it only takes Lance about 25 minutes.

Answer 1

\[\frac{ 1 }{ 40 }+\frac{ 1 }{ 25 } = \frac{ 1 }{ x }\]

Answer 2

What is the Least Common Multiple of 40 and 25?

Answer 3

5

Answer 4

Multiples of 40: 40, 80, 120, ...
Multiples of 25: 25, 50, 75, ...

LCM(40, 25)= ?

Answer 5

BTW, 5 is the Greatest Common Divisor of 40 and 25...

Answer 6

Oops got confused for a second, It is 200 for LCM

Answer 7

OK, so that is used for you new denominator:

\(\dfrac{...}{400}+\dfrac{...}{400}=\dfrac{1}{x}\)

Answer 8

OOPS! Make that 200 instead of 400 :(

Answer 9

Giving you \(\dfrac{5}{200}+\dfrac{8}{200}=\dfrac{1}{x}\)

Answer 10

So\[\frac{ 40 }{ 200 } + \frac{ 25 }{ 200 } = \frac{ }{ x }\]

Answer 11

Oop's forgot to simplify the numerators

Answer 12

No, to get from denominator 40 to 200, you multiplied it with 5, so do the same with the numerator.

Answer 13

Also to get fron denomminator 25 to 200, you had to multiply with 8, so do the same with the numerator...

Answer 14

That is why you get \(\dfrac{5}{200}+\dfrac{8}{200}=\dfrac{13}{200}=\dfrac{1}{x}\)

Answer 15

Once I get to 5/200+8/200=13/200=1/x how do I solve it

Answer 16

13x=200
x=200/13

Answer 17

You almost have the solution: if \(\dfrac{1}{x}=\dfrac{13}{200}\), then \(\dfrac{x}{1}=\dfrac{200}{13}\), so \(x=\dfrac{200}{13} \approx...\)