Irina rode her bike to work at an average speed of 16 miles per hour. It started to rain, so she got a ride home along the same route in her coworker's car at an average speed of 27 miles per hour. If Irina's ride home in the car took 24 minutes (0.4 of an hour), how many hours was her bike ride to work, to the nearest tenth of an hour?

Speed at which Irina traveled home in her coworker's car = 27 miles per hour

Time taken to reach home = 0.4 hour

Then

Distance traveled by Irina in 1 hour = 27 miles

So

Distance traveled by Irina in 0.4 hours = 27 * 0.4 miles

= 10.8 miles

Speed at which Irina traveled to office on her bike = 16 miles per hour

Then

Time taken by Irina to cover 16 miles = 1 hour

So

Time taken by Irina to cover 10.8 miles = (10.8/16) hours

= 0.68 hours

So the time taken by Irina to ride to work is 0.68 hours.