Boats & Streams Quiz 1

Speed downstream = (13 + 4) km/hr = 17 km/hr
Time is taken to travel 68 km downstream = (68/17)=4 hours

Speed upstream = 7.5 kmph.
Speed downstream = 10.5 kmph.
Total time taken =\left ( \frac{105}{7.5}+\frac{105}{10.5}\right )\text{hours}= 24 \text { hours }

Let man's rate upstream be x kmph.
Then, his rate downstream = 2x kmph.
Therefore, (Speed in still water) : (Speed of stream) =\left ( \frac{2x+x}{2}\right ): \left ( \frac{2x-x}{2} \right )
=3:1

Speed downstream = (5 + 1) kmph = 6 kmph.
Speed upstream = (5 - 1) kmph = 4 kmph.
Let the required distance be x km.
Then, \frac{x}{6}+\frac{x}{4}=1
x=2.4 km

Rate downstream =(16/2)=8 kmph
Rate downstream =(16/4)=4 kmph
Speed in still water =\frac{1}{2}\left ( 8+4 \right )=6 \text{ kmph }

Suppose he move 4 km downstream in x hours. Then,
Speed downstream=(4/x) km/hr
Speed upstream=(3/x) km/hr

Therefore, \frac{48}{4/x}+\frac{48}{3/x}=14 \text{ or } x=\frac{1}{2}

Rate of stream=(8-6)/2=1 km/hr

4 km downstream is covered in 15 min.
Therefore,speed of downstream = 16 km/hr.
So speed of upstream = 8km/hr.

Total time taken for downstream journey = 15 min (given). Now total time taken for upstream journey = 8/8 = 1 hr = 60 min.

Hence total time taken from A to B = 15 + 60 = 75 min.

As average speed = Total distance /total time, so average speed from A to B = (12/75)*60 = 48/5 = 9.6kmph.

Speed of boat in still water = x = 5 km/hr.
Let the rate of flow of river = y km/hr.
Therefore, Speed of u/s = 5- y and speed of d / s = 5 + y
Therefore, 90/(5+y) + 90/(5-y) = 100 => y = 4 km/hr.

Time taken to cover total distance = H hrs.
Speed of upstream = s - r. Speed of downstream = s + r.
Therefore, k / (s + r) + k / (s - r) = H => \left ( s^{2}-r^{2} \right )=2sk/H

Speed of upstream = 30 / 6 = 5 km / hr. Speed of man in still water = 6 km / hr.
Therefore, Speed of current = 6 - 5 = 1 km / hr. So speed of downstream = 6 + 1 = 7 km/hr.
Therefore,Distance traveled in 7 hrs = 10 * 7 = 70 km.