boat goes 16 km upstream and 24 km downstream in 6 hours. Also it covers 12 km upstream
and 36 km downstream in the same time. Find the speed of the boat upstream and downstream.
Answers
Answered by
2
Step-by-step explanation:
Let upstream speed = x km/h
And Downstream speed = y km/h
Time taken to cover 16 km in upstream
= 16/x h
Time taken to cover 24 km in downstream
= 24/y h
Total time taken = 6 h
=> upstream time +downstream time = 6h
=> 16/x + 24/y = 6h
=> 2(8/x +12/y) = 6
=> 8/x + 12/y = 3 —----(1)
Again,
Time taken to cover 12 km in upstream
= 12/x h
Time taken to cover 36 km in downstream
= 36/y h
Total time taken = 6 h
=> 12/x + 36/y = 6
=> 6(2/x + 6/y) = 1
=> 2/x + 6/y = 1 - - - - (2)
From equation (1)×1 - (2)×2, we get
8/x + 12/y =3
4/x + 12/ y = 2
-----------------------
8/x - 4/x =3- 2
=> 8 - 4/x = 1
=> 4/x = 1
=> x = 4 km/h
Now, putting the value of x in equation (2)
2/4 +6/y = 1
=> 1/2 + 6/y = 1
=>6/y = 1- 1/2
=> 6/y = 2-1/2
=> 6/y = 1/2
=> y = 6×2
=> y = 12 km/ h
Hence, upstream speed = 4 km/h
Downstream speed = 12 km/h ANS.
Similar questions