Find the speed of the current

Question

A motorboat maintained a constant speed of 30 miles per hour relative to the water in going 36 miles upstream and then returning. The total time for the trip was 2.5 hours. Us this information to find the speed of the current.

Answer 1

v average = (|v up| + |v down|)/2 = d total/ t total = (36 x 2)/ 2.5 = 28.8 miles/hr

 

57.6 = |v up| + |v down|

 

vc = v current

 

v up = v boat - vc = 30 - vc
v down = v boat + vc = 30 + vc

 

60 - 57.6 = 2 vc

vc = 4.8 miles/hr

 

 

Check:

v up = d up/t up = 36/t up = 30 - 4.8 = 25.2 miles/hr

v down = d down/t down = 36/t down = 34.8 miles/hr

 

t up = 1.43 hrs

t down = 1.03 hrs

 

t up + t down = 2.5 = 1.43 + 1.03 = 2.46 = 2.5 hrs