Question 333860
"If susan can pain a house in four hours", then she can paint {{{1/4}}} of a house in 1 hour. So her rate is {{{1/4}}} houses per hour.



If "John can pain a house in six hours", then he can paint {{{1/6}}} of a house in 1 hour. So his rate is {{{1/6}}} houses per hour.



Finally, if "Peter can paint a house in ten hours", then he can paint {{{1/10}}} of a house in one hour, making his rate {{{1/10}}} houses per hour.



So the three rates are: {{{1/4}}}, {{{1/6}}} and {{{1/10}}} houses per hour.



Add them up to get {{{1/4+1/6+1/10=15/60+10/60+6/60=31/60}}}



So their combined rate is {{{31/60}}} houses per hour. In other words, together they can paint {{{31/60}}} of a house in one hour (which is close to 1/2 of a house).


Now multiply this rate by some unknown time 't' to get {{{(31/60)t}}} and set that equal to 1 (since we want to paint <u>one</u> house) to get {{{(31/60)t=1}}}



Next, multiply both sides by 60 to get {{{31t=60}}} and then divide both sides by 31 to isolate t to get {{{t=60/31=1.93548387}}}



So it will take them about 1.935 hours, or close to 2 hours, if they work together.