If it takes 3.5 hours for Mathew to row a distance of X miles up the

1st 2nd statement alone : Insufficient as you will be left with 3 unknowns.

We need both of them to get values for the speed.

Option C

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If it takes 3.5 hours for Mathew to row a distance of X miles up the stream, what is his speed in still water?

(1) It takes him 2.5 hours to cover the distance of X miles downstream.

(2) He can cover a distance of 84 miles downstream in 6 hours.

Let a be the speed in still water.
Let d be the speed of current
hence,
a-d = upstream speed
a+d = downstream speed

speed = distance/time

upstream speed = (a-d)=X/3.5

From 1)
downstream speed = (a+d)=X/2.5 --> 2.5a + 2.5d = X
and we know 3.5a - 3.5d = X
Hence, 3.5a - 3.5d = 2.5a + 2.5d ---> a = 7d --> 2 Variables --> Not sufficient (we can deduce it from the 3 variables and 2 equations only that it will not be sufficient)

From 2) 84 miles in 6 hours downstream
we know, 3.5a - 3.5d = X
a + d = 84/6 = 14 mph --> Not sufficient to find a (still water speed)

Combining 1 and 2,

we have a+d =14, a = 7d ---> Sufficient to find a

Hence C is the answer

let speed of still = a
so
(a+up stream speed )=X/35
find value of a
#1
It takes him 2.5 hours to cover the distance of X miles downstream.
a -down s= X/2.5
sufficient to find value of a
#2
He can cover a distance of 84 miles downstream in 6 hours
insufficient
IMO A

If it takes 3.5 hours for Mathew to row a distance of X miles up the stream, what is his speed in still water?

(1) It takes him 2.5 hours to cover the distance of X miles downstream.

(2) He can cover a distance of 84 miles downstream in 6 hours.

If it takes 3.5 hours for Mathew to row a distance of X miles up the stream, what is his speed in still water?
Let Speed of Mathew = M
Speed of Water = W
Distance given = X
Now, Speed going downstream = M+W
Speed going upstream = M - W
Now, Time taken going upstream = \(\frac{X}{M - W}\)
3.5 = \(\frac{X}{M - W}\)

(1) It takes him 2.5 hours to cover the distance of X miles downstream.
Now, Time taken going downstream = \(\frac{X}{M + W}\)
2.5 = \(\frac{X}{M + W}\)
Hence, 2.5M + 2.5W = 3.5M - 3.5W
M = 6W

Nothing given about specifics.

INSUFFICIENT.

(2) He can cover a distance of 84 miles downstream in 6 hours.
Now, Time taken going downstream = \(\frac{X}{M + W}\)
6 = \(\frac{84}{M + W}\)
M + W = 14

Nothing given about specifics.

INSUFFICIENT.

Together 1 and 2
M = 6W and M + W = 14
M = 12 and W = 2

SUFFICIENT.

Answer C.

Statement (1)
Mathew's upstream speed is \(\frac{X }{ 3.5}\) (miles/hour)
Mathew's downstream speed is \(\frac{X }{ 2.5}\) (miles/hour)
Mathew's speed in still water is \((\frac{X }{ 3.5}+\frac{X }{ 2.5}) : 2\) (miles/hour)
=> Not suff

Statement (2)
=> Mathew's downstream speed is \(\frac{84}{6} = 14\) (miles/hour)
=> Not suff

Combine two statements
\(\frac{X }{ 2.5} = 14\) => X = 35 miles
=>Mathew's speed in still water is \((\frac{35 }{ 3.5}+\frac{35 }{ 2.5}) : 2 = 12\) (miles/hour)
=> Suff

=> Choice C

Time taken to travel X miles upstream = 3.5hrs. We are to determine the speed in still water.
Let Speeed in still water be S, and speed of the stream be St, then speed upstream, Sup, =S-St ----(1), and speed downstream, Sd, = S+St---(2)
(1)+(2) => Sup+Sd=2S, hence S=(Sup+Sd)/2 ----(3)
So to determine S, we need Sup and Sd.

and Speed = Distance/time taken

Statement 1: It takes him 2.5 hours to cover the distance of X miles downstream.
Not sufficient. This is because we don't know X. We need to know X in order to determine Sup and Sd, since we already have the times taken to travel upstream. Statement 1 has also provided the time taken to travel downstream.

Statement 2: He can cover a distance of 84 miles downstream in 6 hours.
From statement 2, we can determine the speed to travel downstream, Sd = 84/6 = 14mph. But since we don't have any information about X, we cannot determine Sup. Statement 2 is insufficient on its own.

1+2
From 1, we know the time taken to cover X miles downstream, and from 2, we know Sd.
so we can determine X=14*2.5 = 35miles.

Now from the question stem, we know that it takes 3.5 hours to travel X miles upstream, hence Sup = 35/3.5 = 10mph

so, S=(10+14)/2 = 12mph.

Both statements when taken together is sufficient.

The answer is C.

Option C:
V=Velocity in still water
Vs= Velocity of stream
X=Distance
V+Vs=X/3.5
FInd V.
A)V-Vs=x/2.5
Can't get ans.
B)V-Vs=84/6
Can't get ans..
Combine A and B, Get value of X and then get Value of V

Interesting one! My first thought about the question is that we'll have two rates: M's speed (in still water), and the speed at which the stream is flowing. Let's say that his speed is M mph, and the stream's speed is S mph.

So, if he's going upstream, the stream's movement will slow him down. The overall speed will then be M - S mph.

If he's going downstream, the overall speed will be M + S mph.

Translate the given information into these terms:

D = R * T
X = (M - S)*3.5
X = 3.5 M - 3.5 S

What is M?

Statment 1: Using the same variables as above, this statement translates into the following equation:

D = R * T

X = (M + S)*2.5
X = 2.5M + 2.5S

I don't think this gives me enough to solve for M, even with the previous equation. Let's try to simplify, just in case. We know that X = 3.5 M - 3.5 S, and we know that X = 2.5 M + 2.5 S.

Therefore,

3.5 M - 3.5 S = 2.5 M + 2.5 S
M = 6 S

But since I don't know S, I can't really solve for M. Not sufficient.

Statement 2: This one gives us more numbers.

D = R * T
84 = (M + S)*6
M + S = 84 / 6 = 14

So, M + S = 14. Also, the given info told us that X = 3.5 M - 3.5 S. Can we solve for M?

S = 14 - M

X = 3.5M - 3.5(14 - M) = 3.5 M - 49 + 3.5 M = 7M - 49

However, I don't know the value of X, so I can't really solve for M. Insufficient again.

Statements 1 and 2 together

Now I have three equations:

X = 3.5 M - 3.5 S (from the given info)
X = 2.5 M + 2.5 S (from statement 1)
M + S = 14 (from statement 2)

That's definitely enough to solve for M, since I have three distinct equations and only three variables. I wouldn't do this on test day, but I'll do it here for the solution:

3.5 M - 3.5 S = 2.5 M + 2.5 S
M = 6S

M + M/6 = 14
7M / 6 = 14
M = 6(14)/7 = 12

Therefore, his speed in still water is 12 mph.

The answer is C.

rt=d, (r-u)=d/3.5

(1) It takes him 2.5 hours to cover the distance of X miles downstream. insufic

(r+u)=d/2.5
(r-u)=d/3.5
2r=d/2.5+d/3.5

(2) He can cover a distance of 84 miles downstream in 6 hours. insufic

(r+u)=84/6=14

(1 & 2) sufic

(r+u)=84/6=14
(r+u)=d/2.5
14=d/2.5, d=35
2r=35/2.5+35/3.5
2r=14+10=24
r=12

Ans (C)

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