A boat covers certain distance between 2 spots in a river taking t1 hrs going downstream and t2 hrs going upstream.what time will be taken by boat to cover same distance in still water?
1 Answer
Explanation:
We're asked to find the expression for the time it takes the boat to travel across the river in still water.
I'll try and show this with a little example:
Suppose a boat is traveling at a constant speed
Going upstream, the true speed of the boat would be
#v_"up" = v+u#
And going downstream, we have
#v_"down" = v-u#
We have our general speed equation:
#v = s/t#
Or in these two cases
#v+u = s/(t_1)#
#v-u = s/(t_2)#
(the distance across the river
The quantity
#u = s/(t_1) - v#
#u = v - s/(t_2)#
So
#color(red)(s/(t_1) - v = v - s/(t_2)#
#2v = s/(t_1) + s/(t_2)#
Here, the speed
#v = s/(t_"still")# :
#(2s)/(t_"still") = s/(t_1) + s/(t_2)#
#2/t_"still" = 1/(t_1) + 1/(t_2)#
#t_"still" = 2/(1/(t_1) + 1/(t_2))#
Get the denominator's fractions into a common denominator:
#t_"still" = 2/((t_2 + t_1)/(t_1t_2))#
or
#color(blue)(ulbar(|stackrel(" ")(" "t_"still" = (2t_1t_2)/(t_1 + t_2)" ")|)#