Question

Lisa takes 3 hours to mow the lawn, while her cousin, Barb, takes 2 hours. How long will it take them working together?

Answer 1

Answer:

$\frac{6}{5}$ $\text{hours}$

Step-by-step explanation:

Given: Lisa takes $3$ hours to mow the lawn, while her cousin, Barb, takes $2$ hours.

To Find: How long will it take them working together.

Solution:

Let total work be  $=\text{w}$

Let total time taken when working together $=\text{T}$

work done by them in one hour when working together $=\frac{\text{w}}{\text{T}}$

Time taken by Lisa to mow the lawn $=3$ $\text{hours}$

work done by Lisa in one hour       $=\frac{\text{w}}{3}$

Time taken by Barb to mow the lawn $=2$ $\text{hours}$

work done by Barb in one hour       $=\frac{\text{w}}{2}$

when working together,

$\text{work done in one hour when working together}=\text{work done by Lisa in one hour}+\text{work done by Barb in one hour}$

putting values

$\frac{\text{w}}{\text{T}}=\frac{\text{w}}{3}+\frac{\text{w}}{2}$

$\frac{\text{w}}{\text{T}}=\frac{5\text{w}}{6}$

$\frac{1}{\text{T}}=\frac{5}{6}$

$\text{T}=\frac{6}{5}$ $\text{hours}$

it will take $\frac{6}{5}$ $\text{hours}$ when working together.

Answer 2

Answer:

5/6 hours= 50 minutes.  

Step-by-step explanation:

We have been given that Lisa takes 3 hours to mow the lawn.

Time taken by Lisa to mow the lawn= 3 hours

Lawn mowed by Lisa in 1 hour = 1/3

Barb, takes 2 hours to mow the same lawn.

Time taken by Barb to mow the lawn= 2 hours

Lawn mowed by Barb in 1 hour = 1/2

Together rates of Barb and Lisa will be 1/3+1/2

We can find time taken by Lisa and Barb, while working together by equating their rates to 1 as they will mow 1 lawn together.

$\frac{1}{3}+\frac{1}{2}=1$

Let us have a common denominator.

$\frac{1*2}{3*2}+\frac{1*3}{2*3}=1$

$\frac{2}{6}+\frac{3}{6}=1$

$\frac{2+3}{6}=1$

$\frac{5}{6}=1$

Therefore, time taken by Barb and Lisa to mow one lawn is 5/6 hours.

We can convert time in minutes by multiplying 5/6 by 60 (1 hour = 60 minutes).

$\frac{5}{6}\times 60=5\times 10= 50$

Therefore, Barb and Lisa can mow the lawn in 50 minutes, if they work together.