SOLUTION: A motorboat can maintain a constant speed of 46 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 48 ​minutes; the return trip takes 44

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Question 1194880: A motorboat can maintain a constant speed of 46 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 48 ​minutes; the return trip takes 44 minutes. What is the speed of the​ current
Found 3 solutions by josgarithmetic, math_tutor2020, MathTherapy:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
Same thing, just all as variables.
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A vehicle can maintain a constant speed of R miles per hour relative to the
water. The vehicle makes a trip upstream to a certain point in U ​minutes; the return trip takes B minutes. What is the speed of the​ current, c ?
------------------------------------------------------------------------------
d, the distance of the "certain trip"
U=48 min
B=44 min
R=46 mph
c, unknown speed of current


system%28R-c=d%2F%28U%2F60%29%2CR%2Bc=d%2F%28B%2F60%29%29

%28U%2F60%29%28R-c%29=d%2C%28B%2F60%29%28R%2Bc%29=d

U%28R-c%29=d%2CB%28R%2Bc%29=d

UR-Uc=BR%2BBc

UR-BR=Bc%2BUc

%28UR-BR%29%2F%28B%2BU%29=c
OR
highlight%28c=R%28%28U-B%29%2F%28U%2BB%29%29%29------and you just plug in the given values and find c.

Many people would choose to use the given values at the beginning, instead of solving the example all in variables.

---------
---------

Usually one would do like so:
              SPEED            TIME          DISTANCE

upstream        (46-c)          (48/60)         d

downstream      (46+c)          (44/60)         d

%2846-c%29%2848%2F60%29=%2846%2Bc%29%2844%2F60%29

%2846-c%29%2848%29=%2846%2Bc%29%2844%29
12%2846-c%29=11%2846%2Bc%29
12%2A46-12c=11%2A46%2B11c
12%2A46-11%2A46=11c%2B12c
46=23c
highlight%28c=2%29

Answer by math_tutor2020(3835) About Me  (Show Source):
You can put this solution on YOUR website!

Upstream = against the current (the boat is slowed down)
Downstream = with the current (the boat is sped up)

c = speed of the current
46-c = speed of the boat going upstream
46+c = speed of the boat going downstream
speeds are in mph

48 minutes = 48/60 = 4/5 hour
44 minutes = 44/60 = 11/15 hour

Upstream:
distance = rate*time
d = r*t
d = (46-c)*(4/5)

Downstream:
d = r*t
d = (46+c)*(11/15)

Equate the two right hand sides and solve for c.
(46-c)*(4/5) = (46+c)*(11/15)
12(46-c) = 11(46+c)
552-12c = 506+11c
-12c-11c = 506-552
-23c = -46
c = (-46)/(-23)
c = 2
In the second step, I multiplied both sides by 15 to clear out the denominators.

Answer: The current has a speed of exactly 2 mph.

Answer by MathTherapy(10810) About Me  (Show Source):
You can put this solution on YOUR website!

A motorboat can maintain a constant speed of 46 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 48 ​minutes; the return trip takes 44 minutes. What is the speed of the​ current
Let speed of current be C
Then overall upstream and downstream speeds are 46 - C, and 46 + C, respectively 
We then get the following DISTANCE equation:  
                                               12(46 - C) = 11(46 + C) ------ Denominators are equal and so are the numerators
                                             12(46) - 12C = 11(46) + 11C
                                          12(46) - 11(46) = 11C + 12C
                                                    1(46) = 23C
                                   Current's speed, or highlight_green%28matrix%281%2C6%2C+C%2C+%22=%22%2C+46%2F23%2C+%22=%22%2C+2%2C+mph%29%29