ron takes two hours more than paul to mow the lawn.
working togather they can mow the lawn in 5 hrs.
how long does it take each of them working alone?
Make this chart:
number of rate as fraction of time required to
lawns mowed lawn mowed per hour mow
Ron
Paul
Both
We are interested in Ron mowing 1 lawn, Paul mowing 1 lawn,
and both working together to mow 1 lawn. So we put 1 for
the number of lawns mowed in all three cases:
number of rate as fraction of time required to
lawns mowed lawn mowed per hour mow
Ron 1
Paul 1
Both 1
Now let "t" equal the time Paul takes to mow 1 lawn. So
put t as Paul's time:
number of rate as fraction of time required to
lawns mowed lawn mowed per hour mow
Ron 1
Paul 1 t
Both 1
>>...ron takes two hours more than paul to mow the lawn...<<
So we add 2 to Paul's time to get Ron's time. So put t+2
for Ron's time:
number of rate as fraction of time required to
lawns mowed lawn mowed per hour mow
Ron 1 t+2
Paul 1 t
Both 1
>>...working togather they can mow the lawn in 5 hrs...<<
So put 5 for the time for both wotking together:
number of rate as fraction of time required to
lawns mowed lawn mowed per hour mow
Ron 1 t+2
Paul 1 t
Both 1 5
Now fill in the rates as fraction of the lawn per hour by dividing
the number of lawns mowed by the time required.
number of rate as fraction of time required to
lawns mowed lawn mowed per hour mow
Ron 1 t+2
Paul 1 t
Both 1 5
We form the equation this way:
Ron's rate + Paul's rate = their combined rate when both work together.
+ =
Can you solve that by getting LCD of 5t(t+1). It's leads to a quadratic
equation that does not factor and you have to use the quadratic
formula. You get two solutions, approximately
t = 9.099019514 and t = -1.099019514 and we ignore the negative one,
so it takes Paul 9.099019514 hours to mow the lawn and it takes
Paul 2 hours more or 11.099019514 hours.
It's either a very huge lawn or they are very slow mowers.
Edwin