A motorboat, whose speed is 15km/h in still water goes 20km downstream and comes back in a total of 4hours. The speed of the stream (in km/h) is:
- A43
- B73
- C63
- D53
Solution & Step-by-step Explanation
Let the speed of the stream be vkm/h.
Speed downstream = 15+v
Speed upstream = 15−v
The total time taken for the round trip is 4 hours:
15+v
20
+
15−v
20
=4
Divide both sides by 4:
15+v
5
+
15−v
5
=1
5(
(15+v)(15−v)
15−v+15+v
)=1
5(
225−v
2
30
)=1
150=225−v
2
v
2
=225−150
v
2
=75⟹v=
75
=5
3
Let's re-verify the options presented in the prompt:
The options given in the source document contain root forms written like 43, 73, 63, 53 with standard radicals missing inside text formatting or matching
75
=5
3
. Let's examine option D which says 53 under square root symbol notation often rendered incorrectly from 5
3
.
5
3
is often written or misread as
75
, or as 5
3
which matches Option D (5\sqrt{3}).
Speed downstream = 15+v
Speed upstream = 15−v
The total time taken for the round trip is 4 hours:
15+v
20
+
15−v
20
=4
Divide both sides by 4:
15+v
5
+
15−v
5
=1
5(
(15+v)(15−v)
15−v+15+v
)=1
5(
225−v
2
30
)=1
150=225−v
2
v
2
=225−150
v
2
=75⟹v=
75
=5
3
Let's re-verify the options presented in the prompt:
The options given in the source document contain root forms written like 43, 73, 63, 53 with standard radicals missing inside text formatting or matching
75
=5
3
. Let's examine option D which says 53 under square root symbol notation often rendered incorrectly from 5
3
.
5
3
is often written or misread as
75
, or as 5
3
which matches Option D (5\sqrt{3}).