Amotorboat maintains a constant speed of 38 miles per hour. it takes 30 minutes to travel upstream and 27 minutes back. what is the speed of current?

r = 2 [stream's speed is 2 mph downstream

Step-by-step explanation:

Remark

The distances traveled [upstream and downstream] are the same.

If it takes longer to go upstream, it means the speed of the current is going against him. So the rate is 38 - r where r is the speed of the current.

The rate of the downstream is 38 + r because it takes him less time to go downstream and the current is helping him go.

The times are given

Givens

Formula

d1 = d2

d1 = (38 - r) * 30

d2 = (38 + r) *27

(38 - r) * 30 = (38+r)*27

Solution

Remove the brackets on both sides.

38*30 - 30*r = 38*27 + 27r                    Add 30r to both sides

38*30 - 30r + 30r =38*27 + 27r + 30r  Combine the numbers

1140 = 1026 + 57r                                   Subtract 1026 from both sides.

114 = 57r                                                  Divide by 57

114/57 = 57r/57

r = 2

answer: the common difference is -0.10