# Shortcut of Boats

Boats
Shortcut 59:
Time taken upstream
$T=\frac D{S_b-S_r}$
Question:
The speed of boat in still water is 40kmph. How long will the boat take to row 175 km upstream in a river of speed 5kmph?
D = 175km
Sb = 40kmph, (speed of boat in still water)
Sr = 5kmph, (speed of river water)
Sb – Sr = 35kmph, (Upstream speed of boat)
Substitute the values in the above formula, we get
T = 175/35
= 5 hours

Shortcut 60:
Time taken to row downstream
$T=\frac D{S_b+S_r}$
Question:
The speed of boat in still water is 30kmph. How long will the boat take to row 96 km downstream in a river of speed 2kmph?
D = 96km
Sb = 30kmph, (speed of boat in still water)
Sr = 2kmph, (speed of river water)
Sb + Sr = 32kmph, (Downstream speed of boat)
Substitute the values in the above formula, we get
T = 96/32
= 3 hours

Shortcut 61:
Speed of boat
$T=\frac{S_{US}+S_{DS}}2$
Question:
Time taken by a boat to row 40km upstream in 4 hours. It took 2 hours to return back to the starting point. Find the speed of the boat and speed of the river.
Step 1: Find the speed upstream and downstream
SUS = 40/4 = 10kmph, (upstream speed)
SDS = 40/2 = 20kmph, (downstream speed)
Step 2: Find the speed of boat and river
Sb = (10 + 20)/2 = 15kmph, (speed of boat)
SUS = Sb – Sr
10 = 15 – Sr
Sr = 5kmph, (speed of river)

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