Question

Jenna can clean the gutters at her house in four hours. Her older brother, John, can clean the gutters in three hours, if they work together, exactly how long would it take them to clean the gutters?

Answer 1

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

The speed of each one is:

$V_1 = \frac{1}{4} g/h\\\\V_2 = \frac{1}{3} g/h$

V = total speed = $\frac{g}{t} = V_1 + V_2$

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 $\frac{7}{12}g/h$ of gutterts for each hour.

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

Finally cleaning together takes 1,714 hours or also

1 hour and 42.8 minutes