Question

a boat covers 24 km upstream and 36 km down stream in 6 hours also it covers 36 km upstream and 24 km down stream in 6 .30 minutes.................


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Answer 1

Answer:

We take the speed of the boat=x km/hr. and that of the water current=y km/hr.

In the first case, their relative speed=x−y upstream & x+y downstream..

UPSTREAM-

The distance=24km.

So the time taken=

x−y

24

.

DOWNSTREAM-

The distance=36km.

So the time taken=

x+y

36

.

∴ the total time taken

=

x−y

24

+

x+y

36

=6(given).

Let x−y=a & x+y=b.

Then the above equation becomes,

24a+36b=6

Or 4a+6b=1.........(i).

In the second case, their relative speed=x−y upstream & x+y downstream..

UPSTREAM-

The distance=36km.

So the time taken=

x−y

36

.

DOWNSTREAM-

The distance=24km.

So the time taken=

x+y

24

.

∴ the total time taken

=

x−y

36

+

x+y

24

=6

2

1

hr.=

2

13

hr(given).

Now we have assumed that x−y=a & x+y=b.

Then the above equation becomes

36a+24b=

2

13

Or 72a+48b=13.........(ii).

(ii)−(iii)⟶60b=5

Or b=

12

1

Or x+y=12.........(iv).

Putting b=

12

1

in (i),

4a+6×

12

1

= 1

Or a=

8

1

Or x−y=8........(v).

Subtracting (iv) from (v),

2y=4

Or y=2km/hr.

So the speed of the current=2km/hr