Word problem

Question

A motorboat has a 4 hour supply of gasoline. How far from the dock can it travel if the rate going out against the current is 20 mph and the rate coming back with the current is 30 mph?

Answer 1

t = time going out at 20 mph ⇒ outward travel distance is 20t

 

4 - t = time coming back at 30 mph ⇒ return travel distance is 30(4 - t)

 

The 2 distances must be the same, so

 

20t = 30(4 - t)

 

50t = 120

 

t = 120/50 hours = 2.4 hours

 

The maximum distance from dock is

 

20t = (20 miles/hour)(2.4 hours) = 48 miles