marth can rake the leaves in her in 4 hours. Her younger brother can do the job in 7 hours. How long will it take them to do the job if they work together

Question

marth can rake the leaves in her in 4 hours. Her younger brother can do the job in 7 hours. How long will it take them to do the job if they work together

 

Answer 1

assign variables:

L = total number of leaves

t = time required

 

We know that Martha's rate is L / 4, and her brother's rate is L / 7

 

The equation for them working together:

(L/4) t  + (L/7) t = L

 

divide both sides by L:

t/4 + t/7 = 1

 

multiply both sides by 28:

7t + 4t = 28

 

11t = 28

 

t = 2.55 hours

Answer 2

x/4+x/7=1

 

find the common factor which 28 in this case

 

x/4+x/7=1/1

 

7x+4x

=====   =28

    28

 

11x=28

x=28/11

 

2 6/11hours

 

6/11*60=33mins (rounding)

 

2hrs and 33mins

 

 

 

Answer 3

If we imagine that the lawn is broken up into 28 blocks, then Marth can complete all 28 blocks in 4 hours, or 7 in one hour.

Her brother can complete 28 blocks in 7 hours, or 4 in one hour.

 

This means every hour they complete 11 blocks together.

 

11x = 28

x = 28/11, or 2 ⁶/₁₁

 

So they will finish in 2 ⁶/₁₁ hours.