hoursince distance = speed × time, we have
(x+3)×1=(x−3)*3/2
=> 2(x + 3) = 3(x-3)
=> 2x + 6 = 3x – 9
=> x = 6+9 = 15 kmph
7. A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 54 km downstream |
A. 5 hours | B. 4 hours |
C. 3 hours | D. 2 hours |
Answer : Option D
Explanation :
Speed of the boat in still water = 22 km/hr
speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 54 km
Time taken = distance/speed=54/27 = 2 hours
8. A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water? |
A. 5 kmph | B. 4.95 kmph |
C. 4.75 kmph | D. 4.65 |
Answer : Option B
Explanation :
Speed downstream = 22/4 = 5.5 kmph
Speed upstream = 22/5 = 4.4 kmph
Speed of the boat in still water = (½) x (5.5+4.42) = 4.95 kmph
9. A man takes twice as long to row a distance against the stream as to row the same distance in favor of the stream. The ratio of the speed of the boat (in still water) and the stream is: |
A. 3 : 1 | B. 1 : 3 |
C. 1 : 2 | D. 2 : 1 |
Answer : Option A
Explanation :
Let speed upstream = x
Then, speed downstream = 2x
Speed in still water = (2x+x)2=3x/2
Speed of the stream = (2x−x)2=x/2
Speed of boat in still water: Speed of the stream = 3x/2:x/2 = 3 : 1
Level 2
1. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is: |
A. 10 | B. 6 |
C. 5 | D. 4 |
Answer : Option C
Explanation :
Speed of the motor boat = 15 km/hr
Let speed of the stream = v
Speed downstream = (15+v) km/hr
Speed upstream = (15-v) km/hr
Time taken downstream = 30/(15+v)
Time taken upstream = 30/(15−v)
total time = 30/(15+v)+30/(15−v)
It is given that total time is 4 hours 30 minutes = 4.5 hour = 9/2 hour
i.e., 30/(15+v)+30/(15−v)=9/2
⇒1(15+v)+1(15−v)=(9/2)×30=3/20
⇒(15−v+15+v)/(15+v)(15−v)=3/20
⇒30/(15*15−v*v)=3/20
⇒30/(225−v*v)=3/20
⇒10/(225−v* v)=1/20
⇒225−v* v =200
⇒v* v =225−200=25
⇒v=5 km/hr
2. 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/hr. | B. 2 km/hr. |
C. 1.5 km/hr. | D. 2.5 km/hr. |
Answer : Option A
Explanation :
Assume that he moves 4 km downstream in x hours
Then, speed downstream = distance/time=4/x km/hr
Given that he can row 4 km with the stream in the same time as 3 km against the stream
i.e., speed upstream = 3/4of speed downstream=> speed upstream = 3/x km/hr
He rows to a place 48 km distant and come back in 14 hours
=>48/(4/x)+48/(3/x)=14
==>12x+16x=14
=>6x+8x=7
=>14x=7
=>x=1/2
Hence, speed downstream = 4/x=4/(1/2) = 8 km/hr
speed upstream = 3/x=3/(1/2) = 6 km/hr
Now we can use the below formula to find the rate of the stream
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water =1/2*(a+b) km/hr
Rate of stream =12*(a−b) km/hr
Hence, rate of the stream = ½*(8−6)=1 km/hr
3. 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. 5 : 6 | B. 6 : 5 |
C. 8 : 3 | D. 3 : 8 |
Answer : Option C
Explanation :
Let the rate upstream of the boat = x kmph
and the rate downstream of the boat = y kmph
Distance travelled upstream in 8 hrs 48 min = Distance travelled downstream in 4 hrs.
Since distance = speed × time, we have
x×(8*4/5)=y×4
x×(44/5)=y×4
x×(11/5)=y— (equation 1)
Now consider the formula given below
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water =1/2(a+b) km/hr
Rate of stream =1/2(a−b) km/hr
Hence, speed of the boat = (y+x)/2
speed of the water = (y−x)/2
Required Ratio = (y+x)/2:(y−x)/2=(y+x):(y−x)=(11x/5+x):(11x/5−x)
(Substituted the value of y from equation 1)
= (11x+5x):(11x−5x)=16x:6x=8:3
4. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? |
A. 3.2 km | B. 3 km |
C. 2.4 km | D. 3.6 km |
Answer : Option C
Explanation :
Speed in still water = 5 kmph
Speed of the current = 1 kmph
Speed downstream = (5+1) = 6 kmph
Speed upstream = (5-1) = 4 kmph
Let the requited distance be x km
Total time taken = 1 hour
=>x/6+x/4=1
=> 2x + 3x = 12
=> 5x = 12
=> x = 2.4 km
5. A man can row three-quarters of a kilometer against the stream in 111⁄4 minutes and down the stream in 71⁄2minutes. The speed (in km/hr) of the man in still water is: |
A. 4 kmph | B. 5 kmph |
C. 6 kmph | D. 8 kmph |
Answer : Option B
Explanation :
Distance = 3/4 km
Time taken to travel upstream = 111⁄4 minutes
= 45/4 minutes = 45/(4×60) hours = 3/16 hours
Speed upstream = Distance/Time= (3/4)/ (3/16) = 4 km/hr
Time taken to travel downstream = 71⁄2minutes = 15/2 minutes = 15/2×60 hours = 1/8 hours
Speed downstream = Distance/Time= (3/4)/ (1/8) = 6 km/hr
Rate in still water = (6+4)/2=10/2=5 kmph
6. 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. 4 mph | B. 2.5 mph |
C. 3 mph | D. 2 mph |
Answer : Option D
Explanation :
Speed of the boat in still water = 10 mph
Let speed of the stream be x mph
Then, speed downstream = (10+x) mph
speed upstream = (10-x) mph
Time taken to travel 36 miles upstream – Time taken to travel 36 miles downstream= 90/60 hours
=>36/(10−x)−36/(10+x)=3/2 =>12/(10−x)−12/(10+x)=1/2 =>24(10+x)−24(10−x)=(10+x)(10−x)
=>240+24x−240+24x=(100−x* x) =>48x=100− (x* x) => x* x +48x−100=0
=>(x+50)(x−2)=0 =>x = -50 or 2; Since x cannot be negative, x = 2 mph
7. At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24-mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour? |
A. 2*1/3 mph | B. 1*1/3 mph |
C. 1*2/3 mph | D. 2*2/3 mph |
Answer : Option D
Explanation :
Let the speed of Rahul in still water be x mph
and the speed of the current be y mph
Then, Speed upstream = (x – y) mph
Speed downstream = (x + y) mph
Distance = 12 miles
Time taken to travel upstream – Time taken to travel downstream = 6 hours
⇒12/(x−y)−12/(x+y)=6
⇒12(x+y)−12(x−y)=6(x*x−y*y)
⇒24y=6(x*x−y*y)
⇒4y= x*x−y*y
⇒x * x =(y* y +4y)⋯(Equation 1)
Now he doubles his speed. i.e., his new speed = 2x
Now, Speed upstream = (2x – y) mph
Speed downstream = (2x + y) mph
In this case, Time taken to travel upstream – Time taken to travel downstream = 1 hour
⇒12/(2x−y)−12/(2x+y)=1
⇒12(2x+y)−12(2x−y)=4*x* x –y* y
⇒24y=4*x* x –y* y
⇒4*x* x = y* y +24y⋯(Equation 2)
(Equation 1 × 4)⇒4x* x =4(y* y +4y)⋯(Equation 3)
(From Equation 2 and 3, we have)
y* y +24y=4(y* y +4y) ⇒y* y +24y=4y* y +16y ⇒3y* y =8y ⇒3y=8
y=8/3 mph i.e., speed of the current = 8/3 mph=2*2/3 mph
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