A boat running upstream takes 6 hours 30 minutes to cover a certain distance, while it takes 3 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Answers
Given : A boat running upstream takes 6 hours 30 minutes to cover a certain distance, while it takes 3 hours to cover the same distance running downstream.
To Find : Ratio between the speed of the boat and speed of the water current respectively
Solution:
Distance = D km
Speed of Boat = S km/hr
Ratio of speeds = 1 : K
Speed of the water current = SK km/hr
Ratio = 1 : K
A boat running upstream takes 6 hours 30 minutes
6 hours 30 minutes = 6.5 hrs = 13/2
=> D/(S - SK) = 13/2
=> D/S(1 - K) = 13/2
=> D/S = 13(1 - K)/2
it takes 3 hours to cover the same distance running downstream.
=> D/(S + SK) = 3
=> D/S = 3(1 + K)
3(1 + K) = 13(1 - K)/2
=> 6(1 + K) = 13(1 - K)
=> 6 + 6K = 13 - 13K
=> 19K = 7
=> K = 7/19
Ratio of speeds = 1 : K
= 1 : 7/19
= 19 : 7
ratio between the speed of the boat and speed of the water current = 19 : 7
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