how long would it take the faster person to do the job?

Question

working together, two people can cut a large lawn in 2 hours. one person can do the job alone in 1 hour less than the other.

Answer 1

Let x be the time in hours it takes for the faster person alone to cut the lawn then x+1 is the time it takes for the slower person to cut it alone.

In one hour the faster person cuts 1/x of the lawn while the slower person cuts 1/(x+1) in an hour.

In two hours they cut the whole lawn. So in one hour working together they cut half the lawn.

Therefore, 1/2=1/x+1/(x+1). Cross multiplying we get: x(x+1)=2(x+1)+2x.

x²+x=2x+2+2x; x²-3x-2=0=(x²-3x+9/4)-9/4-2.

(x-3/2)²=17/4, x=3/2±√17/4=1.5±2.0616. Only the positive root is meaningful: 3.5616 hr approx.

So the faster person can cut the lawn in 3.56 hr approx which is about 3hr 34 min.