MATH SOLVE

4 months ago

Q:
# Bonnie can complete her paper route in 45 min. when her sister jean helps her it takes them 18 min to complete the route. how long would it take jean alone?

Accepted Solution

A:

We know that Bonnie complete her paper route in 45min. So, in 1min she can complete:

[tex]\frac{1}{45}[/tex] of her paper route.

We need to know how long it would take Jean alone, then we will call this time x. Working together they last 18min, so in 1min they can complete:

[tex]\frac{1}{18}[/tex] of the paper route.

The paper route working together satisfies the following equation:

[tex]\frac{1}{18} = \frac{1}{45} + \frac{1}{x}[/tex]

Solving this equation:

[tex]\frac{1}{x} = \frac{1}{18} - \frac{1}{45} = \frac{45-18}{810} = \frac{27}{810}[/tex]

[tex]x = \frac{810}{27} = 30min[/tex]

Finally:

It takes 30min to complete the paper route by Jane alone.

[tex]\frac{1}{45}[/tex] of her paper route.

We need to know how long it would take Jean alone, then we will call this time x. Working together they last 18min, so in 1min they can complete:

[tex]\frac{1}{18}[/tex] of the paper route.

The paper route working together satisfies the following equation:

[tex]\frac{1}{18} = \frac{1}{45} + \frac{1}{x}[/tex]

Solving this equation:

[tex]\frac{1}{x} = \frac{1}{18} - \frac{1}{45} = \frac{45-18}{810} = \frac{27}{810}[/tex]

[tex]x = \frac{810}{27} = 30min[/tex]

Finally:

It takes 30min to complete the paper route by Jane alone.