A person can row downstream 49 km in 7 hours and upstream 36 km in 9 hours. What is the speed of the current?
- A2 km/h
- B3 km/h
- C1.5 km/h
- D2.5 km/h
Solution & Step-by-step Explanation
Let the speed of the boat in still water be u km/h and the speed of the current be v km/h.
Downstream Speed (D):
D=
Time
Distance
=
7
49
=7 km/h
Therefore, u+v=7 ——— (Equation 1)
Upstream Speed (U):
U=
Time
Distance
=
9
36
=4 km/h
Therefore, u−v=4 ——— (Equation 2)
Finding the speed of the current (v):
Subtracting Equation 2 from Equation 1:
(u+v)−(u−v)=7−4
2v=3
v=
2
3
=1.5 km/h
The speed of the current is 1.5 km/h.
Downstream Speed (D):
D=
Time
Distance
=
7
49
=7 km/h
Therefore, u+v=7 ——— (Equation 1)
Upstream Speed (U):
U=
Time
Distance
=
9
36
=4 km/h
Therefore, u−v=4 ——— (Equation 2)
Finding the speed of the current (v):
Subtracting Equation 2 from Equation 1:
(u+v)−(u−v)=7−4
2v=3
v=
2
3
=1.5 km/h
The speed of the current is 1.5 km/h.