PROBLEMS ON BOATS & STREAMS (PART-II)

QUERY 11

A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

A) 2 : 1
B) 3 : 2
C) 8 : 3
D) 5 : 3

MAHA GUPTA
Let the boat’s speed upstream be x km/h and that downstream be y km/h.

So, distance covered upstream = x × 8⁴⁄₅                                     (8 hours 48 minutes = 8⁴⁄₅ hours)
and distance covered downstream = y × 4

But the distance is the same both ways
Thus, x × 8⁴⁄₅ = y × 4
=> y = 11x/5

Therefore the required ratio
(speed downstream + speed upstream)/2 : (speed downstream – speed upstream)/2
=> (y + x)/2 : (y – x)/2
=> y + x : y – x
=> 11x/5 + x : 11x/5 – x
=> 16x/5 : 6x/5
=> 8 : 3 (option ‘C’)

QUERY 12

A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is?

A) 2 mph
B) 2.5 mph
C) 3 mph
D) 4 mph

MAHA GUPTA
Let the speed of the stream x mph.
Thus, speed of the boat downstream = (10 + x) mph
and speed of the boat upstream = (10 – x) mph

Now according to the question
³⁶⁄_{10 – x} – ³⁶⁄_{10 + x} = 90/60                                       (90 minutes = 90/60 hours)
=> 72x × 60 = 90(100 – x2)

=> x² + 48x – 100 = 0

=> (x+ 50)(x – 2) = 0

=> x = 2 mph (option ‘A’)

QUERY 13

Speed of a boat in standing water is 9 km/h and the speed of the stream is 1.5 km/h. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is?

A) 16 hours
B) 18 hours
C) 20 hours
D) 24 hours

MAHA GUPTA
Speed of the boat upstream = 9 – 1.5 = 7.5 km/h
Speed of the boat downstream = 9 + 1.5 = 10.5 km/h

Now the total time taken = time taken upstream + time taken downstream
= ¹⁰⁵⁄_7.5 + ¹⁰⁵⁄_10.5

= 24 hours (option ‘D’)

QUERY 14

A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is?

A) 1 km/h
B) 1.5 km/h
C) 2 km/h
D) 2.5 km/h

MAHA GUPTA
Let time taken by the man to cover the distance downstream or upstream = x hours
Thus, his speed downstream = 4/x  km/h
and his speed upstream = 3/x km/h

Hence, according to the question
48/⁴⁄_x + 48/³⁄_x = 14
=> x = 1/2

Thus man’s speed downstream = 4/x = 8 km/h                (substituting value of x)
and his speed upstream = 3/x = 6 km/h                             (substituting value of x)

Now, the rate of the stream = (speed downstream – speed upstream)/2
= (8 – 6)/2 = 1 km/h (option ‘A’)