Work rate problem?

Question

Lourdes can trim the hedges around her property in 8 hours using an electric hedge trimmer. Rafael can do the same job in 15 hours using a manual trimmer. How long would it take them to trim the hedges working together?

Answer 1

Always work figuring out the portion of the job they can do. So Lourdes can can do 1/8 of the job in an hour. Rafael can do 1/15 of the job in an hour.

Together they can do 1/8 + 1/15 of the job in an hour.
(1/8)x + (1/15)x = 1

Get a common denominator and add.
(15/120 + 8/120)x = 1

(23/120)x = 1

x = 120/23
x = 5.2173913 hours
x = 5 hours 13 minutes 2.61 seconds

Answer 2

Solution

Lourdes can trim the hedges in 8 hours,
Rafael can trim the same hedges in 15 hours.


1 hedge = (Work Rate) x (Time Spent Working)

1 hedge = Work Rate of Lourdes x 8 ; so

work rate of Lourdes is 1/8

1 hedge = Work Rate of Rafael x 15 ; so

work rate of Rafael is 1/15

Plugging these quantities into the main equation above gives the following equation that we need to solve.

1/8t + 1/15t = 1 , get a common denominator

15/120t + 8/120t = 1

23/120t = 1

t = 120/23

t = 5.21739 , so it will take about 5.22 hours for both Lourdes, and Rafael to trim the hedges together.

This is a site that might help you with other rate problems.

http://tutorial.math.lamar.edu/AllBrowsers/1314/LinearApps.asp

Answer 3

these can be fun if you realize you always have to work with the amount done per hour.

Lourdes trims 1/8 of the hedge in 1 hour
Rafael trim 1/15 of the hedge in 1 hour

Working together for x hours, L does 1/8times x or x/8
and R does 1/15 times x or x/15

Together they complete the whole job : 1

x/8+x/15=1
Multiply by the lowest common denominator of 8 and 15: 120

15x+8x=120
23x=120
x=120/23
x=5 and 5/23 hours

Answer 4

The rate for L is 1/8 hedge/hour
The rate for R is 1/15 hedge/hour

Add the rates to get the "together" rate

1/8 + 1/15 = 1/x
15x + 8x = 120 {times 120x}
23 x = 120
x = 120/23

Answer 5

Set the problem up in this format:
1/8+1/15=1/x

Since the common denominator is 120, you want to multiply both sides by 120 to get rid of the fractions:
120(1/8+1/15)=120(1/x)

15+8=120x
23=120x
x=120/23=5 5/23 hours.

I hope this helps!

Answer 6

5 5/23 hrs. = 1/(1/8 + 1/15)