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Darina [25.2K]
3 years ago
10

Jenna can clean the gutters at her house in four hours. Her older brother, John, can clean the gutters in three hours, if they w

ork together, exactly how long would it take them to clean the gutters?
Mathematics
1 answer:
OlgaM077 [116]3 years ago
7 0

Answer:

1 hour and 42.8 minutes

Step-by-step explanation:

To answer this question let's call t_1 while it takes Jenna to clean the gutters

Let's call t_2 while it takes John to clean the gutters

t_1 = 4 h

t_2 = 3 h

t = total time

g = job = 1 (clean the gutters)

The speed of each one is:

V_1 = \frac{1}{4} g/ h

V_2 = \frac{1}{3} g/h

V = V_1 + V_2 = \frac{g}{t} = \frac{1}{t}

So:

V = V_1 + V_2 = \frac{1}{4} +\frac{1}{3}

\frac{1}{t} = \frac{1}{4} + \frac{1}{3}= \frac{7}{12} g/h

t = \frac{12}{7} h

Then, both together paint \frac{7}{12} of gutters for each hour.

This means that it takes \frac{12}{7}  hours to clean the gutters together

Finally cleaning together takes 1,714 hours or also

1 hour and 42.8 minutes

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