The speed of a boat in still water is 6 km/h and the speed of the stream is 1.5 km/h. In going from point A to point B and returning to A, the boatman takes 2 hours 40 min. Find the distance between points A and B.
- A7.5 km
- B8 km
- C7 km
- D8.5 km
Solution & Step-by-step Explanation
Speed of boat in still water (u) = 6km/h
Speed of stream (v) = 1.5km/h
Downstream Speed (D) = u+v=6+1.5=7.5km/h
Upstream Speed (U) = u−v=6−1.5=4.5km/h
Total time taken = 2 hours 40 min=2+
60
40
=2+
3
2
=
3
8
hours
Let the distance between A and B be d.
7.5
d
+
4.5
d
=
3
8
2
15
d
+
2
9
d
=
3
8
15
2d
+
9
2d
=
3
8
2d(
45
3+5
)=
3
8
2d×
45
8
=
3
8
45
2d
=
3
1
2d=15⟹d=7.5km
Speed of stream (v) = 1.5km/h
Downstream Speed (D) = u+v=6+1.5=7.5km/h
Upstream Speed (U) = u−v=6−1.5=4.5km/h
Total time taken = 2 hours 40 min=2+
60
40
=2+
3
2
=
3
8
hours
Let the distance between A and B be d.
7.5
d
+
4.5
d
=
3
8
2
15
d
+
2
9
d
=
3
8
15
2d
+
9
2d
=
3
8
2d(
45
3+5
)=
3
8
2d×
45
8
=
3
8
45
2d
=
3
1
2d=15⟹d=7.5km