Question

Rivka and Sara are sisters and contestants on a survival reality tv show. They must each build a raft that will ultimately carry them off the island. Rivka can build her raft in 5 days. Sara can build her raft in 6 days. Though, as sisters, they sometimes fight, they decided to work together to build their rafts. How many days will it take Rivka and Sara to build their two rafts? (Round your answer to one decimal.)

Answer 1

Rivka's working rate is
x = (1 raft)/(5 days) = 1/5 rafts/day.
Sara's working rate is
y = (1 raft)/(6 days) = 1/6 rafts/day.

When working together, their combined working rate is
x + y = 1/5 + 1/6 = 11/30 rafts/day

The days required to build 2 rafts together is
( 2 rafts)/(11/30 rafts/day) = 60/11 days = 5.45 days

Answer: 5.5 days