Boats and Streams problems

Let the distance he covered each way = d kms

According to the question,

d/45 - d/50 = 1

=> d = 450 kms.

Hence, the total distance he covered in his way = d + d = 2 d = 2 x 450 = 900 kms.

Rate of her upstream = 12/2.5 = 4.8 km/hr

Then, ATQ

Rate of downstream = 4.8 x 3 = 14.4 km/hr

Hence, the distance she covers downstream in 5 hrs = 14.4 x 5 = 72 kms.

Let the place be at a distance of 'd' kms

From the given data,

$$\begin{gathered} d 5 - 1 + d 5 + 1 = 75 60 kms \\ d 4 + d 6 = 5 4 \\ \end{gathered}$$

5d/12 = 5/4 => d = 3 kms.

Hence, the place is 3 kms far.

Speed of the current = 24-16/2

= 8/2

= 4 km/hr.

Let the speed of the boat in still water is 'w'

Speed of the current is 'c'

Let the distance between two places is 'd'

According to the question, motorboat takes half time to cover a certain distance downstream than upstream.

d w + c = 1 2 d w - c

=> 2w - 2c = w + c

=> w = 3c

=> c : w = 1 : 3

Hence, the ratio between rate of current(c) and rate of boat in still water(w) = 1 : 3

Let the speed of current = 'C' km/hr

Given the speed of boat in still water = 6 kmph

Let 'd' kms be the distance it covers.

According to the given data,

Boat takes thrice as much time in going the same distance against the current than going with the current

i.e,  d 8 - C = 3 × d 8 + C

$$\begin{gathered} ? 24 - 3 C = 8 + C \\ ? 4 C = 16 \\ ? C = 4 kmph \end{gathered}$$

Hence, the speed of the current C = 4 kmph.

Speed of boat in still water = 1/2 (12 + 6) = 9 kmph.

Given that, upstream distance = 7 kms

Upstream speed = 7/42 x 60 = 10 kms

Speed of the stream = 3 kmph

Let speed in still water = M kmph, then

Upstream speed = M - 3 = 10

=> M = 13 kmph.

Distance travelled by boat in upstream=24km

Time taken = 6 h

Speed of the boat in upstream = 24/6 = 4 km/h

And distance travelled by boat in downstream = 20 km

Time taken = 4h Speed of the boat in downstream = 20/4 km/h = 5 km/h

Now, speed of the boat in still water = 1/2 [ speed of the boat in upstream + speed of the boat in downstream] =1/2 [4 + 5] = 1/2 × 9 = 4.5 km/h

And speed of the current = 1?2 [speed of the boat in downstream ? speed of the boat in upstream] = 1/2 [5 ? 4] = 1/2 × 1 = 0.5 km/h