Aptitude - Boats and Streams - Discussion
Discussion Forum : Boats and Streams - General Questions (Q.No. 4)
4.
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:
Answer: Option
Explanation:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
 |
30 | + | 30 | = 4 | 1 |
| (15 + x) | (15 - x) | 2 |
 |
900 | = | 9 |
| 225 - x2 | 2 |
9x2 = 225
x2 = 25
x = 5 km/hr.
Video Explanation: https://youtu.be/lMFnNB3YQOo
Discussion:
63 comments Page 7 of 7.
Gayu said:
3 years ago
Someone help me to understand the solution, please.
(3)
Saji said:
3 years ago
(30/15+x) + (30/15-x) =4 (1/2).
By cross multiplying;
(30(15-x) + 30(15+x)) /(15+x) (15-x) = 9/2.
(450-30x+450+30x)/15^2 - x^2 = 9/2.
-30x and +30x get cancelled.
So,
900/15^2 -x^2 = 9/2.
By cross multiplying;
(30(15-x) + 30(15+x)) /(15+x) (15-x) = 9/2.
(450-30x+450+30x)/15^2 - x^2 = 9/2.
-30x and +30x get cancelled.
So,
900/15^2 -x^2 = 9/2.
(5)
Likitha Ganta said:
2 years ago
Speed in still water = 15 km/hr.
Distance traveled in downstream = 30 km.
Time taken in upstream = 4 hr 30 min.
The speed of the stream = ?
Speed = Distance/time.
Distance = 30km.
Speed in upstream = (u-v)km/hr = (15-v)km/hr.
Speed in downstream = (u+v)km/hr = (15+v)km/hr.
Total time = (distance of downstream/speed of downstream) + (distance of upstream/speed of upstream).
30/(15 + x) + 30/(15 - x) = 4 1/2,
30/(15 + x) + 30/(15 - x) = 9/2,
30(15 - x) + 30(15 + x) = 9/2 * (15 - x)(15 + x),
900 = 9/2 * (225 + 15x - 15x - x^ 2),
900 = 9/2 * (225 - x ^ 2),
1800= 9(225 - x ^ 2),
1800 = 2025 - 9x ^ 2,
2025 - 1800 = 9x ^ 2,
225 = 9x ^ 2,
x ^ 2 = 225/9 = 25,
x = √(25) = 5.
Ans=>X=5.
Distance traveled in downstream = 30 km.
Time taken in upstream = 4 hr 30 min.
The speed of the stream = ?
Speed = Distance/time.
Distance = 30km.
Speed in upstream = (u-v)km/hr = (15-v)km/hr.
Speed in downstream = (u+v)km/hr = (15+v)km/hr.
Total time = (distance of downstream/speed of downstream) + (distance of upstream/speed of upstream).
30/(15 + x) + 30/(15 - x) = 4 1/2,
30/(15 + x) + 30/(15 - x) = 9/2,
30(15 - x) + 30(15 + x) = 9/2 * (15 - x)(15 + x),
900 = 9/2 * (225 + 15x - 15x - x^ 2),
900 = 9/2 * (225 - x ^ 2),
1800= 9(225 - x ^ 2),
1800 = 2025 - 9x ^ 2,
2025 - 1800 = 9x ^ 2,
225 = 9x ^ 2,
x ^ 2 = 225/9 = 25,
x = √(25) = 5.
Ans=>X=5.
(6)
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