A motor boat takes 6hours to cover 100km downstream and 30 km upstream if the boat goes 75 km upstream and 75 km downstream find the speed of the boat in still water and find the speed of the stream
Answers
Step-by-step explanation:
⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇
▶⏩ Let the speed of the boat in still water be x km/hr.
and, the speed of the boat in stream be y km/hr. Then,
↪➡ Speed upstream= ( x - y ) km/hr.
↪➡ and, speed downstream = ( x + y ) km/hr.
▶⏩ Time taken to cover 30km upstream
▶⏩ Time taken to cover 24km downstream
▶⏩ Total time taken = 6hrs.
▶⏩ Again, time taken to cover 75km upstream
( Returning 75km back from 75km downstream).
▶⏩ Time taken to cover 75km downstream
▶⏩ Total time taken 8hrs.
in equation (1) and (2), we get:-)
↪➡ 30u + 100v = 6.
↪➡ 15u + 50v = 3.....................(3)
and,
↪➡ 75u + 75v = 8.....................(4)
▶⏩ Multiply by 5 in equation (3).
we get,
↪➡ 75u + 250v = 15....................(5)
▶▶ Substract in equation (4) and (5).
75u + 250v = 15
75u + 75v = 8
(-)......(-)...........(-)
______________
=> 175v = 7.
▶⏩ Put the value of ‘v’ in equation (3).
and,
▶⏩ Substract equation (6) and (7).
x - y = 15
x + y = 25
(-)...(-)....(-)
_________
=> -2y = -10
▶⏩ Now, put the value of ‘y’ in equation (6).
↪➡ x - 5 = 15.
↪➡ x = 15 + 5.
✅✅Hence, the speed of motorboat in still water is 20 km/hr.
and , the speed of motorboat in stream is 5 km/hr.✔✔
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