Working together, Pat, Lindsey, and Robin can dig a drainage ditch in 2 hours. Working alone, Robin can do it in 6 hours, while Pat can do it 2 1/4 hours faster than Lindsay. How long will it take Lindsay to dig the ditch by herself? (Round your answer to two decimal places.)
Please help me solve this problem. Thank you very much!
Make this chart:
Number of Digging rate
ditches Hours in
dug Required ditches/hour
Pat digging alone
Lindsey digging alone
Robin diggin alone
All three digging together
Let the answer be x, which is the number of hours required for Lindsay
to dig ONE ditch, so we put x for Lindsay's hours required and 1 for
the number of ditches.
Number of Digging rate
ditches Hours in
to dig Required ditches/hour
Pat digging alone
Lindsey digging alone 1 x
Robin diggin alone
All three digging together
>>...Pat can do it hours faster than Lindsay...<<
So we put Pat's time as x - and 1 ditch to dig. We SUBTRACT
because "faster" means LESS time.
Number of Digging rate
ditches Hours in
to dig Required ditches/hour
Pat digging alone 1 x-
Lindsey digging alone 1 x
Robin diggin alone
All three digging together
Similar, since all the other information is about digging ONE ditch,
fill in 1 for the number of ditches to dig in the other two cases.
Also fill in the given number of hours required in each case:
Number of Digging rate
ditches Hours in
to dig Required ditches/hour
Pat digging alone 1 x-
Lindsey digging alone 1 x
Robin diggin alone 1 6
All three digging together 1 2
Next we fill in the digging rates in ditches/hour by dividing the
number of ditches by the hours:
Number of Digging rate
ditches Hours in
to dig Required ditches/hour
Pat digging alone 1 x-
Lindsay digging alone 1 x
Robin diggin alone 1 6
All three digging together 1 2
The equation comes from:
+ + =
+ + =
Let's first simplify
Change the mixed fraction to an improper fraction = .
Multiply top and bottom by 4:
So the equation becomes:
+ + =
Solve that by clearing of fractions by multiplying through by the
LCD of 6x(4x-9)
You will get 7.329001404 which we round to 7.33 hours
It takes Robin approximately 7.33 hours to dig one ditch.
Edwin