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2 years ago

Please help! Solve the following:

Mathematics

1 answer:

mihalych1998 [28]2 years ago

4 0

Answer:

n=10.

Step-by-step explanation:

$\frac{45}{n^{2}-3n-4 }$ - $\frac{3}{n-4}$ = $\frac{2}{n+1 }$

$\frac{45}{n^{2}-3n-4 }$ - $\frac{3(n+1)}{(n+1)(n-4)}$ = $\frac{2(n-4)}{(n+1)(n-4) }$

$\frac{45}{n^{2}-3n-4 }$ - $\frac{3n+3}{n^{2} -3x-4}$ = $\frac{2n-8}{n^{2} -3x-4 }$

45-3n-3=2n-8

45-3+8=5n

n=50/5=10

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<h3>Answer: 24 minutes</h3>

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Explanation:

Let's say the lawn is 120 square feet. I picked 120 as it is the LCM (lowest common multiple) of 60 and 40.

Since Wilma can mow the lawn in 60 minutes, her rate is 120/60 = 2 sq ft per minute. In other words, each minute means she gets 2 more square feet mowed. Rocky can do the full job on his own in 40 minutes, so his rate is 120/40 = 3 sq ft per minute.

Their combined rate, if they worked together (without slowing each other down), would be the sum of the two rates. So we get 2+3 = 5 sq ft per minute as the combined rate. The total time it would take for this 120 sq ft lawn is 120/5 = 24 minutes.

--------------------------

Another approach

Wilma takes 60 minutes to do the full job, so her rate is 1/60 of a lawn per minute. Rocky's rate is 1/40 of a lawn per minute. Their combined rate is

1/60 + 1/40 = 2/120 + 3/120 = 5/120 = 1/24 of a lawn per minute

x = number of minutes

(combined rate)*(time) = number of jobs done

(1/24)*x = 1

x = 1*24

x = 24 is the time it takes if they worked together without getting in each other's way.

Effectively, we are solving the equation

1/A + 1/B = 1/C

with

A = time it takes Wilma to do the job on her own

B = time it takes Rocky to do the job on his own

C = time it takes the two working together to get the job done

The equation above is equivalent to C*(1/A + 1/B) = 1 or (1/A + 1/B)*C = 1.

So basically you find the value of 1/A + 1/B, then find the reciprocal of this to get the value of C.

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