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STD
Alpha400/kk400
Beta400/(k-2.5)k-2.5400


Speed of Alpha < Speed of beta

Checking options
1. 400/k = 25 => k = 16
k-2.5 = 13.5
400/13.5 all options are integers, this doesn't work

2. 400/k = 32 => k = 12.5
k - 2.5 = 10
400/10 = 40
This works
Speed = 32 and 40

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Two cargo ships, Ship Alpha and Ship Beta, transport goods along a 400-nautical-mile channel. Ship Alpha makes the journey in k hours. Ship Beta makes the same journey in (k - 2.5) hours.

In the table, select for Ship Alpha a possible average speed (in nautical miles per hour) and select for Ship Beta a possible average speed (in nautical miles per hour) that would be jointly consistent with the given information. Make only two selections, one in each column.
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Distance = 400 nautical miles

Ship Alpha: -
Time taken = k hours
Average speed (Sa) = 400/k nautical miles per hour

Ship Beta: -
Time taken = k - 2.5 hours
Average speed (Sb) = 400/(k-2.5) hours

Case 1: Sa = 400/k = 25; k =400/25 = 16 hours; k-2.5 = 13.5 hours; Sb = 400/13.5 = 29.62; Not an option
Case 2: Sa = 400/k = 32; k = 400/32 = 12.5 hours; k -2.5 = 10 hours; Sb = 400/10 = 40 ; Feasible

Ship Alpha32
Ship Beta40
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Two cargo ships, Ship Alpha and Ship Beta, transport goods along a 400-nautical-mile channel. Ship Alpha makes the journey in k hours. Ship Beta makes the same journey in (k - 2.5) hours.

In the table, select for Ship Alpha a possible average speed (in nautical miles per hour) and select for Ship Beta a possible average speed (in nautical miles per hour) that would be jointly consistent with the given information. Make only two selections, one in each column.
D=400nm
Ship Alpha Speed=vA; Time = (400/vA)
Ship Beta Speed=vB; Time=(400/vB)
400/vB=(400/vA)-2.5
Trying Options:
SA's speed =30nm/h
Time=400/30=12.5
SB's Time = 12.5-2.5=10
SB's Speed = 400/10 = 40.
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Two cargo ships, Ship Alpha and Ship Beta, transport goods along a 400-nautical-mile channel. Ship Alpha makes the journey in k hours. Ship Beta makes the same journey in (k - 2.5) hours.

In the table, select for Ship Alpha a possible average speed (in nautical miles per hour) and select for Ship Beta a possible average speed (in nautical miles per hour) that would be jointly consistent with the given information. Make only two selections, one in each column.


distance is 400
time difference is 2.5 hours

plug in values and test where condition is met..

if speed of A is 32 then time 12.5 hours

speed of B will be 400/(12.5-2.5) ; 40

32; 40 is correct option
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Let speed of Alpha be A and that of Beta be B

Using the formula Distance / Speed = Time, it is given that,

(400 / A) - (400 / B) = 2.5
=> (1 / A) - (1 / B) = 1/160

Putting the options in the above equation
A = 32, B = 40

(1 / 32) - (1 / 40) = 1 / 160
=> (5 - 4) / 160 = 1 / 160
=> 1/160 = 1/160
This fits perfectly

Hence, speed of Alpha = 32
Speed of Beta = 40
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Distance = Speed*Time
Total distance = 400 nautical miles
Alpha time = k hours
Beta time = k-2.5 hours
Time difference between two ships is exactly 2.5 hours and beta speed is faster as it take less time than alpha
Time = 400/speed
From choices check different speeds
25; 400/25=16
32; 400/32=12.5
40; 400/40=10
50; 400/50=8
64; 400/64=6.25
80; 400/80=5
Only 12.5 and 10 times have difference of 2.5 hours.
Possible speeds are 32 and 40
We know ship Beta is faster so, Beta speed = 40 and Alpha speed = 32

Ship Alpha = 32
Ship Beta = 40
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say alpha speed X
beta speed Y
time for alpha= k hrs
time for beta= k-2.5 hrs

speed for X= 400/k
speed for Y =400/k-2.5

from choices
when X= 32, k=12.5 and y=40
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Two cargo ships, Ship Alpha and Ship Beta, transport goods along a 400-nautical-mile channel. Ship Alpha makes the journey in k hours. Ship Beta makes the same journey in (k - 2.5) hours.

In the table, select for Ship Alpha a possible average speed (in nautical miles per hour) and select for Ship Beta a possible average speed (in nautical miles per hour) that would be jointly consistent with the given information. Make only two selections, one in each column.
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Since D is const
st (Alpha) = st (Beta)
S(beta) > S(alpha) since t(alpha)>t(beta) indirect proportion when D is same

Now S(alpha)*k=S(beta)*(k-2.5)
Is S(alpha) = 32 nautical miles per hr it would take 12.5 hrs for alpha to complete the journey
So Ship Beta will take 10hrs for the journey, thus S(beta)=40 nautical miles per hr
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Two cargo ships, Ship Alpha and Ship Beta, transport goods along a 400-nautical-mile channel. Ship Alpha makes the journey in k hours. Ship Beta makes the same journey in (k - 2.5) hours.

In the table, select for Ship Alpha a possible average speed (in nautical miles per hour) and select for Ship Beta a possible average speed (in nautical miles per hour) that would be jointly consistent with the given information. Make only two selections, one in each column.
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Given that distance is 400 miles and speed of k and k-2.5 hrs

Average speed for ship alpha =400/k and ship beta =400/k-2.5

Trying out different options from the available choices, if 400/k=32 then k= 12.5

400/(12.5-2.5) =40

Therefore, Ship Alpha =32 and Ship Beta = 40
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let speed of alpha be S2 & speed of beta S1
K*S2=400
K*S2=(K-2.5)*S1

As S2<S1,
start using options..
if S2=32,K=12.5
&S1=40 (Available option)

Ans 32 & 40
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I solved the question by trying each option, considering that the speed of ship A must be lower then the speed of ship B.

400/25 = 16
400/32 = 12.5
400/40 = 10 -> 10 = 12.5 - 2.5

There is always only one right answer, I selected 32 and 40 as the answers.

To be quicker at making the divisions, I factored 400 = 2^4 * 5^2
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total distance is 400
time taken by ship alpha is k hrs
time taken by ship beta is k-2.5 hrs
substituting the speed value
we get 400/32=12.5 hrs=k
400/10=40 which is speed of beta

hence 32 and 40 are the answer
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Speed of Alpha is 400/k take each speed for alpha find value of k & calculate 400/(k-2.5) if it's in option then that would be answer. Alpha speed 32 gives value 400/k = 32 ---> k = 12.5 hence 400/(12.5 - 2.5) = 40 So alpha speed 32 & Beta 40.
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Two cargo ships, Ship Alpha and Ship Beta, transport goods along a 400-nautical-mile channel. Ship Alpha makes the journey in k hours. Ship Beta makes the same journey in (k - 2.5) hours.

In the table, select for Ship Alpha a possible average speed (in nautical miles per hour) and select for Ship Beta a possible average speed (in nautical miles per hour) that would be jointly consistent with the given information. Make only two selections, one in each column.
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Given Distance = 400 nautical miles Ship Alpha time = k hours
Ship Beta time = k − 2.5 hours
Speed = Distance / Time
Alpha speed = 400 /k
Beta speed = 400 /k − 2.5
Since Beta takes less time, Beta must be faster than Alpha.
From Alpha = k = 400/Va
So Beta's time: (k - 2.5) = (400/Va) - 2.5
Which should be equal to 400/Vb
(400/Va) = (400/Vb) - 2.5

Now test values using the values given in Table:
If Va = 25, Vb comes around 30. Not a match.

If we put Va = 32, Vb comes to be around 40. Exact match.
Hence
Va = 32 and Vb = 40.

If we put
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Two cargo ships, Ship Alpha and Ship Beta, transport goods along a 400-nautical-mile channel. Ship Alpha makes the journey in k hours. Ship Beta makes the same journey in (k - 2.5) hours.

In the table, select for Ship Alpha a possible average speed (in nautical miles per hour) and select for Ship Beta a possible average speed (in nautical miles per hour) that would be jointly consistent with the given information. Make only two selections, one in each column.
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Alpha's speed A= 400/k & Beta's speed B= 400/k-2.5

400/A = k & 400/B = k-2.5

I tried putting values for A to find k, used that to find k-2.5 and checked if 400/k-2.5 gave any value given in the options

For A = 32, 400/32 = 12.5, giving k-2.5 = 10, and 400/10 = 40 as B

For rest 400/k-2.5 wont give any value as given in the options.

Ans 32, 40
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Two cargo ships, Ship Alpha and Ship Beta, transport goods along a 400-nautical-mile channel. Ship Alpha makes the journey in k hours. Ship Beta makes the same journey in (k - 2.5) hours.

In the table, select for Ship Alpha a possible average speed (in nautical miles per hour) and select for Ship Beta a possible average speed (in nautical miles per hour) that would be jointly consistent with the given information. Make only two selections, one in each column.
The two cargo ships alpha and beta travel a distance of 400 nautical mile.

The time taken by the ships alpha and beta are k and (k-2.5) hrs respectively.

The speed of the ships alpha and beta are Sa and Sb respectively.

Difference of time = 2.5 hrs

(400/Sa) - (400/Sb) = 2.5

If we put Sa = 25, then time = (400/25) =16 hrs.

So, the time taken by beta is (16-2.5) = 13.5 (No such option exists).

If, we put Sa = 32 , then time taken = (400/32)=12.5

Then the time taken by ship Beta = 12.5 - 2.5 = 10 hrs.

Speed Sb = (400/10) = 40 ( Option Exists).

Thus, Sa = 32, and Sb = 40.
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Let average speed of ship alpha be S(a) and average speed for Ship Beta be S(b).

S(a) = 400/k

S(b) = 400/(k-2.5)

Only one combination make it consistent which is S(a) = 32 , S(b) = 40

So average speed shop alpha is 32 and average speed for Ship Beta is 40.
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Two cargo ships, Ship Alpha and Ship Beta, transport goods along a 400-nautical-mile channel. Ship Alpha makes the journey in k hours. Ship Beta makes the same journey in (k - 2.5) hours.

In the table, select for Ship Alpha a possible average speed (in nautical miles per hour) and select for Ship Beta a possible average speed (in nautical miles per hour) that would be jointly consistent with the given information. Make only two selections, one in each column.
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