Gardeners 5542

Three gardeners mow the meadow for a while. Four gardeners can do it half an hour earlier. How long will it take five gardeners to do it?

Correct answer:

x =  1.2 h

Step-by-step explanation:


3t = a
4 (t-0.50) = a
5 x= a

3·t = a
4·(t-0.50) = a
5·x= a

a-3t = 0
a-4t = -2
a-5x = 0

Row 2 - Row 1 → Row 2
a-3t = 0
-t = -2
a-5x = 0

Row 3 - Row 1 → Row 3
a-3t = 0
-t = -2
3t-5x = 0

Pivot: Row 2 ↔ Row 3
a-3t = 0
3t-5x = 0
-t = -2

Row 3 - -1/3 · Row 2 → Row 3
a-3t = 0
3t-5x = 0
-1.667x = -2


x = -2/-1.66666667 = 1.2
t = 0+5x/3 = 0+5 · 1.2/3 = 2
a = 0+3t = 0+3 · 2 = 6

a = 6
t = 2
x = 6/5 = 1.2

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