# Math Question! Have fun.?

If John can mow a the lawn in 4 hours and John and George together can mow it in 2 1/2 hours. Then how long does it take George to mow it by himself?

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• Steven
Lv 7
9 years ago

if a does it in a certain time

and b does it in a certain time

1/a+1/b=1/c

[still waiting for someone to tell me why it works]

John =4

total =2 1/2=5/2

1/J+1/G=1/(5/2)

1/4+1/G=2/5

1/G=2/5-1/4

1/G=8/20-5/20

1/G=3/20

G=20/3

George takes 6 2/3 hours to mow the lawn himself

• 9 years ago

(time together / time alone1) + (time together / time alone2) = 1

(5/2 / 4) + (5/2 / x) = 1

5/(2x) = 1 - 5/8 = 3/8

2x = 5 / (3/8) = 5(8/3) = 40/3

x = 20/3

It takes George 6 hours and 40 minutes to mow the lawn by himself.

• Anonymous
9 years ago

Well I'd like to say 4 hours but it didn't half when old George came along so it might take longer , cause technically half the lawn takes John 2 hours , sounds like George is slow so must have taken him the two hours to do his half, by then johns done then starts helping him , so I'm gonna go with 5 hours 15 mins

• 9 years ago

You've got to subtract the rates. John is 1/4=0.25 lawns per hour, Together they do 1/2.5 0.4 lawns per hour.

So George alone does 0.4 - 0.25 = 0.15 lawns per hour. This will take take 1/0.15 = 6 2/3 hours or 6 hours and 40 minutes.

• naveed
Lv 4
9 years ago

formula is

1/combined time=1/john time+1/mow time

1/2.5=1/4+1/x

1/2.5-1/4=1/x

0.4-.25=1/x

0.15=1/x

or

x=1/0.15

x=6.67 hours

so mow alone will take 6.67 hours to complete the job. hope it helps take care

• 9 years ago

1 and 1/4.

• TC
Lv 7
9 years ago

x + y = 1

4x + y = 5/2

y = - x + 1

4x - x + 1 = 5/2

3x = 5/2 - 2/2

3x = 3/2

x = 3/6 = 1/2 hour

x + y = 1

1/2 + y = 1

y = 1/2

1/2 hour

• Mike G
Lv 7
9 years ago

2.5*1/4 + 2.5G = 1

2.5 + 10G = 4

10G = 1.5

G = 0.15 lawns/hour

G takes 1/0.15 = 6.67 hours

• 9 years ago

4 hrs, why should it take any longer than John?

No math involved at all in this question.