Aptitude - Boats and Streams - Discussion
Discussion Forum : Boats and Streams - General Questions (Q.No. 8)
8.
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:
Answer: Option
Explanation:
Let the speed of the stream x mph. Then,
Speed downstream = (10 + x) mph,
Speed upstream = (10 - x) mph.
 |
36 | - | 36 | = | 90 |
| (10 - x) | (10 + x) | 60 |
72x x 60 = 90 (100 - x2)
x2 + 48x - 100 = 0
(x+ 50)(x - 2) = 0
x = 2 mph.
Discussion:
85 comments Page 2 of 9.
Faria said:
4 years ago
Convert 90 minutes into hours, therefore 90/60 = 3/2 hours,
Given that, the speed of the boat in still water = 10,
Let, speed of the stream = x,
Then,
Downstream = 10+x,
Upstream = 10-x.
According to the condition,
3/2 (10-x) = (10+x),
So, 15-1.5x = 10+x,
So, 2.5x = 5,
So, x = 2 (ans).
Given that, the speed of the boat in still water = 10,
Let, speed of the stream = x,
Then,
Downstream = 10+x,
Upstream = 10-x.
According to the condition,
3/2 (10-x) = (10+x),
So, 15-1.5x = 10+x,
So, 2.5x = 5,
So, x = 2 (ans).
(14)
Oni said:
8 years ago
36/(10-x)-36/(10+x) = 90/60,
=> 36/(10-x)-36/(10+x) = 3/2,
=> 12/(10-x)-12/(10+x) = 1/2,
=> 12(10+x)-12(10-x)/(10-x)(10+x) = 1/2,
=> 24(10+x)-24(10-x) = (10-x)(10+x),
=> 48x = 100-x^2,
=> x^2+50x-2x-100 = 0,
=> (x+50)(x-2) = 0,
=> x = 2.
=> 36/(10-x)-36/(10+x) = 3/2,
=> 12/(10-x)-12/(10+x) = 1/2,
=> 12(10+x)-12(10-x)/(10-x)(10+x) = 1/2,
=> 24(10+x)-24(10-x) = (10-x)(10+x),
=> 48x = 100-x^2,
=> x^2+50x-2x-100 = 0,
=> (x+50)(x-2) = 0,
=> x = 2.
Bala said:
1 decade ago
Answer: Option A.
Explanation:
Let the speed of the stream x mph. Then,
Speed downstream = (10+x) mph,
Speed upstream = (10-x) mph.
= 36-36 = 90.
= (10 - x)(10 + x)60.
= 72x x 60 = 90(100 - x2).
x2 + 48x - 100 = 0.
(x+ 50)(x - 2) = 0.
x = 2 mph.
Explanation:
Let the speed of the stream x mph. Then,
Speed downstream = (10+x) mph,
Speed upstream = (10-x) mph.
= 36-36 = 90.
= (10 - x)(10 + x)60.
= 72x x 60 = 90(100 - x2).
x2 + 48x - 100 = 0.
(x+ 50)(x - 2) = 0.
x = 2 mph.
Needa said:
4 years ago
72x / 100 - x^2 = 90/60.
72x * 60 = 90 *(100-x^2),
72x * 60 = 9000 - 90x^2,
Dividing throughout by 90.
(72x * 60) / 90 = 9000/90 - 90x^2.
48x = 100 - x^2.
x^2 + 48x - 100 = 0.
x^2 +50x - 2x -100 = 0.
x(x + 50) -2(x + 50) = 0.
(x + 50) (x-2) = 0.
72x * 60 = 90 *(100-x^2),
72x * 60 = 9000 - 90x^2,
Dividing throughout by 90.
(72x * 60) / 90 = 9000/90 - 90x^2.
48x = 100 - x^2.
x^2 + 48x - 100 = 0.
x^2 +50x - 2x -100 = 0.
x(x + 50) -2(x + 50) = 0.
(x + 50) (x-2) = 0.
Akash said:
6 years ago
@Siddesh.
Boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream.
It means while going downstream the time will be less and will while going upstream (i.e against) it will take 90 min more;
so t=d/s.
Boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream.
It means while going downstream the time will be less and will while going upstream (i.e against) it will take 90 min more;
so t=d/s.
Rohit chavan said:
1 decade ago
Given Condition:(upstream speed-(90/60)min)=downstream speed;
we know,
time=distance/speed;
(90/60)min=(upstream distance/upstream speed)+
(downstream distance/downstream speed)
(90/60)min=(36/(10-x))+(36/(10+x));
we know,
time=distance/speed;
(90/60)min=(upstream distance/upstream speed)+
(downstream distance/downstream speed)
(90/60)min=(36/(10-x))+(36/(10+x));
Rohit Chavan said:
1 decade ago
Downstream speed = (upstream speed-90); _____(because downstream takes 90 min less then upstream.)
Hence, (90/60)min=(36/(10-x))+(36/(10+x));
and proceed as given in solution i.e. simplify the equation.
Hence, (90/60)min=(36/(10-x))+(36/(10+x));
and proceed as given in solution i.e. simplify the equation.
Sharayu said:
4 years ago
36/(10+x) - 36/(10-x) = 90/60.
Take 36common.
36((10+x)-(10-x))/100-x2 = 9/6.
Solve term.
36*2x/100-x2 = 9/x.
Cross multiple the terms,
72x*6 = 900-9x2.
X2+48x-100 = 0.
Take factor,
Get two term x=-50 & x=2.
Take 36common.
36((10+x)-(10-x))/100-x2 = 9/6.
Solve term.
36*2x/100-x2 = 9/x.
Cross multiple the terms,
72x*6 = 900-9x2.
X2+48x-100 = 0.
Take factor,
Get two term x=-50 & x=2.
(2)
Kalpana said:
9 years ago
Given.
(up_stream time) - (down_stream time) = 90mins.
36(miles)/(10-x) - 36/(10+x) = 90/60.
We get equation form of
x^2 + 48x - 100 = 0.
Hence, x = 2 and x = -50.
x = 2 is the answer.
(up_stream time) - (down_stream time) = 90mins.
36(miles)/(10-x) - 36/(10+x) = 90/60.
We get equation form of
x^2 + 48x - 100 = 0.
Hence, x = 2 and x = -50.
x = 2 is the answer.
Likitha Ganta said:
2 years ago
Speed downstream = (10 + x) * m/h.
Speed upstream = (10 - x) m/h.
36/(10 - x) - 36/(10 + x) = 90/60.
72** 60 = 90(100 - x ^ 2).
x ^ 2 + 48x - 100 = 0.
(x + 50)(x - 2) = 0.
x = 2m/h.
Speed upstream = (10 - x) m/h.
36/(10 - x) - 36/(10 + x) = 90/60.
72** 60 = 90(100 - x ^ 2).
x ^ 2 + 48x - 100 = 0.
(x + 50)(x - 2) = 0.
x = 2m/h.
(2)
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