Word problems

Question

if Angela were to paint her living room alone it would take her 5 hours. Her sister Fran could do the job in seven hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if need.

Answer 1

If Angela can paint a room in 5 hours, then after one hour, she's ¹/₅ finished.

If Fran can paint a room in 7 hours, then after one hour, she's ¹/₇ finished.

After one hour, together they're ¹/₅ + ¹/₇ finished

¹/₅ + ¹/₇ → ⁷/₃₅ + ⁵/₃₅ = ¹²/₃₅

 

¹²/₃₅ h = 1 (after so many hours, they finish the one room)

Isolate h, and you'll have the number of hours.