I can paint a house in 5 hours thus my rate is 1/5 houses per hour

my friend can paint a house in 6 hours thus his rate is 1/6 houses per hour

let x = the number of hours we need to paint the house together thus the together rate is 1/x houses per hour

1/5 + 1/6 = 1/x

by solving we find

x = 30/11 hr

x = 2 8/11 hr = 2 hr 8*60/11 min = 2 hr 43 min 7*60/11 sek = 2 hr 43 min 38 sek

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it would take us 2 hr 43 min and 38 sek to paint the house together.