A motor boat goes down the stream 30 km and again returns to the
starting point in a total time of 4 hours and 30 minutes. If the speed of the
stream is 5 km/hr, then find the speed of the motor boat in still water.
Answers
ANSWER
It is given that speed of motor boat in still water is 15 km/hr and total distance travelled is 30 km.
Let the speed of the stream be x km/hr then the speed upstream is (15−x) km/hr and speed downstream is (15+x) km/hr.
It is also given that total time taken is 4 hours 30 minutes, therefore,
Time taken to row down the stream is
15+x
30
and
Time taken to row up the stream is
15−x
30
Thus, we have
15+x
30
+
15−x
30
=4
2
1
⇒
15+x
30
+
15−x
30
=
2
9
⇒
(15+x)(15−x)
30(15−x)+30(15+x)
=
2
9
⇒
(15)
2
−x
2
450−30x+450+30x
=
2
9
(∵a
2
−b
2
=(a+b)(a−b))
⇒
225−x
2
900
=
2
9
⇒2×900=9(225−x
2
)
⇒1800=9(225−x
2
)
⇒225−x
2
=
9
1800
⇒225−x
2
=200
⇒x
2
=225−200
⇒x
2
=25
⇒x=±
25
⇒x=±5
Since the speed cannot be negative thus, x=5.
Hence, the speed of the stream is 5 km/hr.