SOLUTION: A boat traveled 260 miles downstream and back. The trip downstream took 13 hours. he trip back took 26 hours. Find the speed of the boat in still water and the speed of the current

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Question 1146100: A boat traveled 260 miles downstream and back. The trip downstream took 13 hours. he trip back took 26 hours. Find the speed of the boat in still water and the speed of the current
Found 3 solutions by Theo, greenestamps, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
r * t = d
r = rate
t = time
d = distance

b = the rate of the boat
c = the rate of the current

going with the current, r = b + c
going against the current, r = b - c

your formulas become:

with the current:
(b + c) * t = d

against the current:
(b - c) * t = d

d - 259 nukes
t = 13 hours going with the current.
t = 26 hours going against the current.

your formulas become:

with the current:
(b + c) * 13 = 260

against the current:
(b - c) * 26 = 260

simplify both formulas to get:
13b + 13c = 260
26b - 26c = 260

these two equations need to be solved simultaneously.

multiply both sides of the first equation by 2 and leave the second equation as is to get:
26b + 26c = 520
26b - 26c = 260

add both equations together to get:
52b = 780

solve for b to get:
b = 780/52 = 15

in the first of the two equations, replace b with 15 and solve for c.
start with 13b + 13c = 260
replace b with 15 to get 13*15 + 13c = 260
simplify to get 195 + 13c = 260
subtract 195 from both sides to get:
13c = 65
solve for c to get c = 65/13 = 5

replace b with 15 and c with 5 in both original equations to get:
13b + 13c = 13*15 + 13*5 = 195 + 65 = 260
26b - 26c = 26*15 - 26*5 = 390 - 130 = 260

b = 15 and c = 5 are confirmed to be good values.
your solution is that the rate of the boat is 15 miles per hour and the rate of the current is 5 miles per hour.





Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The solution from the other tutor is valid; but it is way more work than is necessary.

Note that the statement of the problem allows two possible interpretations -- 130 miles each direction for a total of 260 miles, or 260 miles each direction.

I will go with the same interpretation as the other tutor: 260 miles each direction.

Then the downstream speed is 260/13 = 20mph and the upstream speed is 260/26 = 10mph.

Now we have a very common type of problem that is easily solved.

We have a boat speed and a river current speed; the sum of the two (going downstream, with the current) is 20mph, and the difference (going upstream, against the current) is 10mph.

Either simple algebra or even simpler logical reasoning tells us the two speeds are 15mph and 5mph.

ANSWER: boat speed 15mph; current speed 5mph
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
A boat traveled 260 miles downstream and back. The trip downstream took 13 hours. he trip back took 26 hours. Find the speed of the boat in still water and the speed of the current
Let speed of boat in still water and current speed be S, and C, respectively

Then for the DOWNSTREAM-TRIP, we get the following AVERAGE SPEED equation: 

And, for the UPSTREAM-TRIP, we get the following AVERAGE SPEED equation: 

2S = 30 ------ Adding eqs (ii) & (i)

S, or speed of boat in still water = 



15 + C = 20 ------- Substituting 15 for S in eq (i)

C, or speed of current =  

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