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The total time taken by a boat to cover (d + 320) km distance in downstream and (d - 400) km distance in upstream is ‘t’ hours. The same boat can cover ‘d’ distance in still water in 38.4 hours. The total time taken by the same boat to cover (d - 96) km distance in downstream and ‘d’ distance in upstream is ( t + 18.5) hours. If the speed of stream is 24 km/h, then find out the time taken by the same boat to cover (d+64) km distance downstream.
- a)20 hours
- b)25 hours
- c)30 hours
- d)35 hours
- e)None of above
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The total time taken by a boat to cover (d + 320) km distance in down...
Let’s assume the speed of the boat in still water is B and the speed of the stream is C.
The total time taken by a boat to cover (d+320) km distance in downstream and (d-400) km distance in
upstream is ‘t’ hours.
The same boat can cover ‘d’ distance in still water in 38.4 hours.
The total time taken by the same boat to cover (d - 96) km distance in downstream and ‘d’ distance in upstream is (t + 18.5) hours.
Now put Eq.(ii) in the above equation.
If the speed of stream is 24 km/h.
C = 24
Now put the value of C in the Eq.(iv).
After solving the above equation, we will get B = −40.864865, 40.
Negative value of B is not possible. So B = 40 km/h
Now put the value of B in Eq.(ii).
d = 38.4B = 38.4 × 40 = 1536 km
Time taken by the same boat to cover (d+64) km distance downstream = 
= 25 hours
Hence, option b is the correct answer.
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Community Answer
The total time taken by a boat to cover (d + 320) km distance in down...
To solve this problem, let's break it down into steps:
Step 1: Define variables
Let's define the variables:
- d: distance covered by the boat in still water (in km)
- t: total time taken by the boat (in hours)
- s: speed of the boat in still water (in km/h)
- c: speed of the stream (in km/h)
Step 2: Calculate the speed of the boat in downstream and upstream
The speed of the boat in downstream is the sum of the speed of the boat in still water and the speed of the stream:
Speed downstream = s + c
The speed of the boat in upstream is the difference between the speed of the boat in still water and the speed of the stream:
Speed upstream = s - c
Step 3: Calculate the time taken to cover the given distances
In the first scenario, the boat covers a distance of (d - 320) km downstream and (d - 400) km upstream. The time taken for these distances can be calculated using the formula: time = distance / speed.
Time downstream = (d - 320) / (s + c)
Time upstream = (d - 400) / (s - c)
In the second scenario, the boat covers a distance of (d - 96) km downstream and d km upstream. The time taken for these distances can be calculated using the same formula.
Time downstream = (d - 96) / (s + c)
Time upstream = d / (s - c)
Step 4: Set up and solve the equations
We are given that the total time taken in the first scenario is t hours, and the total time taken in the second scenario is (t + 18.5) hours.
Using this information, we can set up the following equations:
(t = Time downstream + Time upstream)
(t + 18.5 = Time downstream + Time upstream)
By substituting the expressions for time downstream and time upstream from step 3 into the equations above, we can solve for the variables.
Step 5: Find the time taken to cover (d + 64) km downstream
Once we have the values of d, s, and c, we can calculate the time taken to cover (d + 64) km downstream using the formula: time = distance / speed.
Substitute the values of d, s, and c into the formula to find the time taken.
The correct answer is option 'B' - 25 hours.
Step 1: Define variables
Let's define the variables:
- d: distance covered by the boat in still water (in km)
- t: total time taken by the boat (in hours)
- s: speed of the boat in still water (in km/h)
- c: speed of the stream (in km/h)
Step 2: Calculate the speed of the boat in downstream and upstream
The speed of the boat in downstream is the sum of the speed of the boat in still water and the speed of the stream:
Speed downstream = s + c
The speed of the boat in upstream is the difference between the speed of the boat in still water and the speed of the stream:
Speed upstream = s - c
Step 3: Calculate the time taken to cover the given distances
In the first scenario, the boat covers a distance of (d - 320) km downstream and (d - 400) km upstream. The time taken for these distances can be calculated using the formula: time = distance / speed.
Time downstream = (d - 320) / (s + c)
Time upstream = (d - 400) / (s - c)
In the second scenario, the boat covers a distance of (d - 96) km downstream and d km upstream. The time taken for these distances can be calculated using the same formula.
Time downstream = (d - 96) / (s + c)
Time upstream = d / (s - c)
Step 4: Set up and solve the equations
We are given that the total time taken in the first scenario is t hours, and the total time taken in the second scenario is (t + 18.5) hours.
Using this information, we can set up the following equations:
(t = Time downstream + Time upstream)
(t + 18.5 = Time downstream + Time upstream)
By substituting the expressions for time downstream and time upstream from step 3 into the equations above, we can solve for the variables.
Step 5: Find the time taken to cover (d + 64) km downstream
Once we have the values of d, s, and c, we can calculate the time taken to cover (d + 64) km downstream using the formula: time = distance / speed.
Substitute the values of d, s, and c into the formula to find the time taken.
The correct answer is option 'B' - 25 hours.
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The total time taken by a boat to cover (d + 320) km distance in downstream and (d - 400) km distance in upstream is ‘t’ hours. The same boat can cover ‘d’ distance in still water in 38.4 hours. The total time taken by the same boat to cover (d - 96) km distance in downstream and ‘d’ distance in upstream is ( t + 18.5) hours. If the speed of stream is 24 km/h, then find out the time taken by the same boat to cover (d+64) km distance downstream.a)20 hoursb)25 hoursc)30 hoursd)35 hourse)None of aboveCorrect answer is option 'B'. Can you explain this answer?
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