Shortcut - Boats
Shortcut–Boats
Time taken to row upstream: Time taken to row upstream=$\dfrac{D_{us}}{S_{b}-S_{r}}$
$D_{us}$– Distance travelled upstream.
$S_{b}$ – Speed of the boat in still water.
$S_{r}$ – Speed of the river flow (or) stream (or) current.
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?
Answer: D = 175km
$S_{b}$= 40kmph, (speed of boat in still water)
$S_{r}$ = 5kmph, (speed of river water)
$S_{b}-S_{r}$ = 35kmph, (Upstream speed of boat)
Substitute the values in the above formula, we get
T = 175/35
= 5 hours
Shortcut–Boats
Time taken to row downstream:
Time taken to row downstream=$\dfrac{D_{ds}}{S_{b}+S_{r}}$
$D_{ds} $– Distance travelled downstream.
$S_{b}$– Speed of the boat in still water.
$S_{r}$– Speed of the river flow (or) stream (or) current.
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?
Answer: D = 96km
$S_{b}$ = 30kmph, (speed of boat in still water)
$S_{r}$= 2kmph, (speed of river water)
$S_{b}+ S_{r} $= 32kmph, (Downstream speed of boat)
Substitute the values in the above formula, we get
T = 96/32
= 3 hours
Shortcut–Boats
Finding speed of the boat when upstream and downstream speed are known.
Speed of the boat $S_{b}=\dfrac{S_{ds}+S_{us}}{2}$
$S_{b}$ – Speed of the boat in still water.
$S_{us}$ - Upstream speed.
$S_{ds}$– Downstream speed.
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.
Answer: Step 1: Find the speed upstream and downstream.
$S_{us}$= 40/4 = 10kmph
$S_{ds}$= 40/2 = 20kmph
Step 2: Find the speed of boat.
$S_{b}$= (10 + 20)/2 = 15kmph
Shortcut–Boats
Finding speed of the river when upstream and downstream speed are known.
Speed of the boat,$S_{b}=\dfrac{S_{ds}-S_{us}}{2}$
$S_{b}$ – Speed of the boat in still water.
$S_{us}$ - Upstream speed.
$S_{ds}$– Downstream speed.
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 the river.
Answer: Step 1: Find the speed upstream and downstream
$S_{us}$ = 40/4 = 10kmph
$S_{ds}$ = 40/2 = 20kmph
Step 2: Find the speed of the river
$S_{r}$= (20 – 10)/2 = 5kmph