Answer:
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
