Question 188529: A boat took one hour and 50 minutes to go 55km downstream and 3 hours, 40 minutes to return. Find the boat's rate in still water and the rate of the current
answer: the rate of the boat in still water is 22 1/2 mph; the rate of the current is 7 1/2 mph.
need a full break down of how my text book got this answer
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A boat took one hour and 50 minutes to go 55km downstream and 3 hours, 40 minutes to return. Find the boat's rate in still water and the rate of the current
------------------
1 hr = 6/6 hr ; 50 minutes = 5/6 hr ; So 1 hr 50 = 11/6 hr
3 hrs = 9/3 hr ; 40 minutes = 2/3 hr ; So 3 hr 40 min = 11/3 hr
--------------------------------
Downstream DATA:
distance = 55 km ; time = (11/6) hr. ; rate = d/t = 55/(11/6) = 30 kph
--------------------
Upstream DATA:
distance = 55 km ; time = (11/3) hr. ; rate = d/t = 55/(11/3) = 15 kph
----------------------
Equations:
b + c = 30 kph
b - c = 15 kph
------------------
Add to solve for "b":
2b = 45 kph
b = 22.5 kph (speed of the boat in still water)
---
Substitute to solve for "c":
22.5 + c = 30
c = 30-22.5 = 7.5 kph ( speed of the current)
===================================================
Cheers,
San H.
|
|
|
