A Cruise ship goes downstream 250 km from Kanpur to Allahabad in 5 hours. Cruise speed in still water is 40 km/hr. Find the time taken by cruise when it Returned to Kanpur at the same speed.a)550 minsb)500 minsc)480 minsd)450 minsCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
Distance traveled downstream = 250 km
Time taken downstream = 5 hours
Cruise speed in still water = 40 km/hr

To find:
Time taken by the cruise to return to Kanpur

Formula:
Speed = Distance/Time

Explanation:
Let's assume the speed of the stream is 'x' km/hr.

When the cruise is traveling downstream, the effective speed is the sum of the cruise speed in still water and the speed of the stream. So, the effective speed downstream is (40 + x) km/hr.

Using the formula Speed = Distance/Time, we can calculate the time taken downstream:
Time taken downstream = Distance traveled downstream / Effective speed downstream

Time taken downstream = 250 km / (40 + x) km/hr

Since the time taken downstream is given as 5 hours, we can write the equation:
5 = 250 / (40 + x)

Solving the above equation for x, we get:
40 + x = 250 / 5
40 + x = 50
x = 10

So, the speed of the stream is 10 km/hr.

As the cruise is returning upstream, the effective speed is the difference between the cruise speed in still water and the speed of the stream. So, the effective speed upstream is (40 - x) km/hr.

Using the formula Speed = Distance/Time, we can calculate the time taken upstream:
Time taken upstream = Distance traveled upstream / Effective speed upstream

Since the distance traveled upstream is the same as downstream (250 km), we can write the equation:
Time taken upstream = 250 km / (40 - x) km/hr

Substituting the value of x, we get:
Time taken upstream = 250 km / (40 - 10) km/hr
Time taken upstream = 250 km / 30 km/hr
Time taken upstream = 8.33 hours

Converting the time taken to minutes, we get:
Time taken upstream = 8.33 hours * 60 minutes/hour
Time taken upstream = 500 minutes

Therefore, the time taken by the cruise to return to Kanpur at the same speed is 500 minutes, which is option B.

Answer

Given:-

Distance between Kanpur and Allahabad = 250 km

Cruise Speed in still water(v) = 40 km/hr

Time taken when goes downstream = 5 hours

Formula used:-Time = Distance/Speed

Calculation:-Let the stream velocity be u,

When goes downstream,

Relative speed = v + u = 40 + u

⇒ 5 = 250/(40 + u)

⇒ 200 + 5u = 250

⇒ u = 50/5 = 10 km/hr = Speed of stream

When goes upstream,

Relative speed = v - u = 40 - 10 = 30 km/hr

∴ Time = 250/30

Time = 8.34 hours

Time is taken = 8.34 × 60 = 500 mins

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