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.
Joan said:
1 decade ago
Please explain how you have got (x+50) (x-2).
Chandhu said:
1 decade ago
Speed=distance/time.
They had given that, the time difference between upstream and downstream as 90 min or 90/60 hours.
We know the relation that: speed=distance/time.
From that time=distance/speed.
Therefore: upstream time-downstream time= (upstream distance/upstream speed) - (downstream distance/downstream speed).
Which is equal to:.
90/60 hours= (36/10-X) - (36/10+X). (X=speed of stream).
From this by solving the equation we can get the X value as 2 miles/hour).
Therefore speed of stream=2 miles/hour (mph).
They had given that, the time difference between upstream and downstream as 90 min or 90/60 hours.
We know the relation that: speed=distance/time.
From that time=distance/speed.
Therefore: upstream time-downstream time= (upstream distance/upstream speed) - (downstream distance/downstream speed).
Which is equal to:.
90/60 hours= (36/10-X) - (36/10+X). (X=speed of stream).
From this by solving the equation we can get the X value as 2 miles/hour).
Therefore speed of stream=2 miles/hour (mph).
Sag said:
1 decade ago
How to solve the equation.
Actually I forget to solve these equations.
How they got x2 + 48x - 100 = (x+50)(x-2).
Actually I forget to solve these equations.
How they got x2 + 48x - 100 = (x+50)(x-2).
Kavitha said:
1 decade ago
(x+ 50)(x - 2) = 0 how this step come from x2 + 48x + 100 = 0.
This equations please explain?
This equations please explain?
Gopal said:
1 decade ago
Downstream-upstream = ((36/(10+x)) - ((36/(10-x)) ;
I have tried with this I got clarification if any one has any doubt check with this.
Thank you.
I have tried with this I got clarification if any one has any doubt check with this.
Thank you.
Guru said:
1 decade ago
Two roots of eqn are 2 and -50.
We can't take -ve root so 2 is the answer.
Hence the equation (x+ 50)(x - 2) = 0 from x2+ 48x + 100 = 0.
We can't take -ve root so 2 is the answer.
Hence the equation (x+ 50)(x - 2) = 0 from x2+ 48x + 100 = 0.
Sandeep said:
1 decade ago
In 4th problem '+' is used why '-' hear.
36/(10 - x) "-" 36/(10 + x) = 90/60.
36/(10 - x) "-" 36/(10 + x) = 90/60.
Puneeth kumar k said:
1 decade ago
Because in question they have mentioned that 90min less.
Shubh said:
1 decade ago
Sorry but I am not able to understand as to how the equation 72x x 60 = 90 (100 - x2) is reduced into x2 + 48x + 100 = 0.
Could you explain in more detail?
Could you explain in more detail?
Sowmya said:
1 decade ago
Take 36 common,
36(1/(10-x)-1/(10+x)) = 90/60.
36((10+x)-(10-x))/(100-x2) = 3/2 since in Denominator is in the form (a+b)(a-b) = a2-b2.
And 90/60 = 2/3.
36((10+x-10+x)/100-x2 = 3/2.
36(2x/100-x2) = 3/2.
72x/100-x2 = 3/2.
hence 72x*2 = 3(100-x2).
3x2+144x-300 = 0.
x2+48x-100 = 0.
(x+ 50)(x - 2) = 0.
x = 2 mph.
Hope you understand guys.
36(1/(10-x)-1/(10+x)) = 90/60.
36((10+x)-(10-x))/(100-x2) = 3/2 since in Denominator is in the form (a+b)(a-b) = a2-b2.
And 90/60 = 2/3.
36((10+x-10+x)/100-x2 = 3/2.
36(2x/100-x2) = 3/2.
72x/100-x2 = 3/2.
hence 72x*2 = 3(100-x2).
3x2+144x-300 = 0.
x2+48x-100 = 0.
(x+ 50)(x - 2) = 0.
x = 2 mph.
Hope you understand guys.
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