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Boat b takes 10 hours to cover certain distance in a river (both upstream and downstream) while boat p takes 12 hours for the same journey. Find the ratio of the speed of boat b to the speed of boat p.
- a)5 : 6
- b)6 : 5
- c)3 : 5
- d)Cannot be determined
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Boat b takes 10 hours to cover certain distance in a river (both upstr...
Let the total distance covered by these boats be x and the speed of the stream be s.
Let the speed of boat b and boat p be b and p kmph respectively
x / b - s + x / b + s = 10 ...(i)
x / p - s + x / b + s = 12 ...(ii)
Dividing (i) by (ii),
b / p (p2 - s2 / b2 - s2) = 10 / 12 = 5 / 6
From this equation, the ratio of the speed of boat b to the speed of boat p cannot be determined.
Hence, option 4.
Let the speed of boat b and boat p be b and p kmph respectively
x / b - s + x / b + s = 10 ...(i)
x / p - s + x / b + s = 12 ...(ii)
Dividing (i) by (ii),
b / p (p2 - s2 / b2 - s2) = 10 / 12 = 5 / 6
From this equation, the ratio of the speed of boat b to the speed of boat p cannot be determined.
Hence, option 4.
Most Upvoted Answer
Boat b takes 10 hours to cover certain distance in a river (both upstr...
Given:
- Boat B takes 10 hours to cover a certain distance in a river (both upstream and downstream).
- Boat P takes 12 hours for the same journey.
To find:
The ratio of the speed of Boat B to the speed of Boat P.
Approach:
- Let the speed of Boat B be 'b' and the speed of Boat P be 'p'.
- The upstream speed of Boat B would be (b - r) and the downstream speed would be (b + r), where 'r' is the speed of the river.
- The upstream speed of Boat P would be (p - r) and the downstream speed would be (p + r).
- We know that the distance covered by both boats is the same.
Calculation:
- Let's assume the distance covered by both boats is 'd'.
- According to the given information, Boat B takes 10 hours to cover the distance 'd'.
- The time taken by Boat B to cover the distance upstream is 'd/(b - r)' and the time taken downstream is 'd/(b + r)'.
- The total time taken by Boat B is given as 10 hours, so we have the equation:
d/(b - r) + d/(b + r) = 10 ...(1)
- Similarly, the total time taken by Boat P is given as 12 hours, so we have the equation:
d/(p - r) + d/(p + r) = 12 ...(2)
- We need to find the ratio b:p, so we divide equation (1) by equation (2):
[d/(b - r) + d/(b + r)] / [d/(p - r) + d/(p + r)] = 10/12
- Simplifying the equation, we get:
(p^2 - b^2) / (p^2 + b^2) = 1/6
- Cross multiplying, we get:
6(p^2 - b^2) = p^2 + b^2
- Simplifying further, we get:
5p^2 = 7b^2
p^2/b^2 = 7/5
p/b = √(7/5)
- Since we cannot determine the exact values of p and b, the ratio p:b cannot be determined.
- Therefore, the correct answer is option (D) Cannot be determined.
- Boat B takes 10 hours to cover a certain distance in a river (both upstream and downstream).
- Boat P takes 12 hours for the same journey.
To find:
The ratio of the speed of Boat B to the speed of Boat P.
Approach:
- Let the speed of Boat B be 'b' and the speed of Boat P be 'p'.
- The upstream speed of Boat B would be (b - r) and the downstream speed would be (b + r), where 'r' is the speed of the river.
- The upstream speed of Boat P would be (p - r) and the downstream speed would be (p + r).
- We know that the distance covered by both boats is the same.
Calculation:
- Let's assume the distance covered by both boats is 'd'.
- According to the given information, Boat B takes 10 hours to cover the distance 'd'.
- The time taken by Boat B to cover the distance upstream is 'd/(b - r)' and the time taken downstream is 'd/(b + r)'.
- The total time taken by Boat B is given as 10 hours, so we have the equation:
d/(b - r) + d/(b + r) = 10 ...(1)
- Similarly, the total time taken by Boat P is given as 12 hours, so we have the equation:
d/(p - r) + d/(p + r) = 12 ...(2)
- We need to find the ratio b:p, so we divide equation (1) by equation (2):
[d/(b - r) + d/(b + r)] / [d/(p - r) + d/(p + r)] = 10/12
- Simplifying the equation, we get:
(p^2 - b^2) / (p^2 + b^2) = 1/6
- Cross multiplying, we get:
6(p^2 - b^2) = p^2 + b^2
- Simplifying further, we get:
5p^2 = 7b^2
p^2/b^2 = 7/5
p/b = √(7/5)
- Since we cannot determine the exact values of p and b, the ratio p:b cannot be determined.
- Therefore, the correct answer is option (D) Cannot be determined.
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Boat b takes 10 hours to cover certain distance in a river (both upstream and downstream) while boat p takes 12 hours for the same journey. Find the ratio of the speed of boat b to the speed of boat p.a)5 : 6b)6 : 5c)3 : 5d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?
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