On a bright Sunday morning three A, B and C decided to go on a river for fishing and boating. They decided to leave for the place together in the evening. The journey was smooth, it just went as scheduled then they reached to the river, and started to set the boat on sail. They were enjoying their ride with full speed. They started boating form a place to another place which is at a distance of 42 km and then again returns to the starting place. They took 20 hours in all. The time taken by them riding downstream in going 14 km is equal to the time taken by them riding upstream in going 6 km. For calculating they took speed of the boat in still water as x km/hr and speed of the river as y km/hr. Based on the above information, answer the following questions:
Step-by-step explanation:
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Given : boating from a place to another place which is at a distance of 42 km and then again returns to the starting place. They took 20 hours in all. The time taken by them riding 14km downstream is equal to the time taken by them riding 6 km upstream
To Find : Boat speed in still water
River speed
Upstream speed
Solution:
D = 42 km
Speed in still water = x km/hr
Speed of stream / river = y km/hr
Upstream speed = x – y km/hr
Down stream speed = x + y km/hr
They took 20 hours in all
=> 42/(x – y) + 42/(x + y) = 20
=> 42( 2x ) = 20 ( x +y)(x – y)
=> 21x = 5 ( x + y)(x -y)
The time taken by
them riding 14km downstream is equal to the time taken by them riding 6 km
=> 14/ (x + y) = 6/(x – y)
=> 7/ (x + y) = 3/(x- y)
=> 7 x- 7y = 3x + 3y
=> 4x = 10y
or y = 2x/5
21x = 5 ( x + 2x/5)(x – 2x/5)
=> 21x = 5 ( 7x/5)(3x/5)
=> x = 5
y = 2
Boat speed in still water = 5 km/hr
Speed of the river = 2 km/hr
Upstream speed = 5 – 2 = 3 km/hr
Downstream speed = 5 + 2 = 7 km/hr
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