SOLUTION: A boat traveled 280 miles downstream and back. The trip downstream took 14 hours. The trip back took 140 hours. Find the speed of the boat in still water and the speed of the curre

Question 1202398: A boat traveled 280 miles downstream and back. The trip downstream took 14 hours. The trip back took 140 hours. Find the speed of the boat in still water and the speed of the current.
Found 3 solutions by math_helper, mananth, josgarithmetic:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

Downstream: V = v + c
where
V = total speed,
v = speed of boat in still water, and
c = speed of current
V = 280mi/14hr = 20mi/hr
This tells us
v + c = 20 (1)

For the upstream direction, we subtract the speed of the current:
v - c = 280/140
v - c = 2 (2)

Add (1) and (2): 2v = 22 --> v = 11 --> c = 9 (plug v=11 into (1) or (2))
Ans:
Speed of boat in still water is 11mi/hr
Speed of current is 9mi/hr

This solution does make the assumption that the speed of the boat and the speed of the current add / subtract in a straightforward (linear) manner.

Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

Let boat speed =x mph in still water
Let current speed =y mph
against current x-y time taken 140.00 hours
with wind x+y time taken 14.00 hours

Distance = same= 140 miles
t=d/r
Upstream time equation

140 / ( x - y )= 140.00
Downstream time equation
140.00 /( x + 1 y) = 14.00
x 1y = 1.00 ....................1
140 / ( x- y )= 14.00
140 /( x - 1 y) = 14.00
x - y = 10.00 ...............2
Multiply (1) by 1.00
Multiply (2) by 1.00
we get
x + y = 1
x - y = 10
2 x = 11

/ 2

x = 5.5 mph

plug value of x in (1)

x - y = 1
5.5 - y = 1.00
-y = 1.00 -5.5
-1 y = -4.50
y = 4.5 mph
Complete by writing the answer

Answer by josgarithmetic(39629)   (Show Source): You can put this solution on YOUR website!

DIRECTION SPEED TIME DIST. Downstr r+c 14 280 Upstr r-c 140 280 TOTAL

boat speed without current, 11 mph.
current's speed, 9 mph.
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