Question 637732
Use the formula d = rt.
Where d is the distance travelled (miles)
r is the rate of travel (miles/hour)
t is the time of travel (hours)
Downstream your rate is the speed of the boat (b) PLUS the speed of the current (c) for a net speed of (b+c). Upstream the current is "working" against the boat so the net speed is (b-c).
Downstream equation
d = (b+c)*t, applying the given values for the downstream trip yields
(1) 252 = (b+c)*14
Upstream equation
d = (b-c)*t, applying the given values for the upstream trip yields
(2) 252 = (b-c)*21
Now solve (1) and (2) simultaneously
(1) b+c = 252/14 = 18
(2) b-c = 252/21 = 12
Add (1) and (2)
(b+c)+(b-c) = 18 + 12
2b +0 = 30
b = 15
(1) 15 + c = 18
c = 3
Correct? Let's check.
Is (252=(15+3)*14)?
Is (252=18*14)?
Is (252=252)? Yes
Is (252=(15-3)*21)?
Is (252=12*21)?
Is (252=252)? Yes
Answer: The speed of the boat in still water is 15 mph and the speed of the current is 3 mph