Question

The difference between downstream and upstream speed is 2 kmph and the total time taken during upstream and downstream is 2 hours. What is the upstream speed, if the downstream and upstream distance are 2 km each

Answer 1

2/x + 2/(x+2) = 2.

x2 – 2 = 0

x = 1.414kmph

Answer 2

Answer:

Here we will find the Upstream speed using the difference between downstream and upstream speed is 2 kmph, total time taken during upstream and downstream is 2 hours and the downstream and upstream distance are 2 km each. Answer: Upstream speed: $1.414kmph$.

Step-by-step explanation:

Let upstream speed      = u kmph

     downstream speed = d kmph

Difference between downstream and upstream speed is 2 kmph

                         ∴   d - u $=2 kmph$

                                    d $=2+u$  ----------------(1)

Time taken during upstream and downstream is 2 hours and downstream and upstream distance are 2 km each.

Already we know the formula, $Time = \frac{Distance}{Speed}$.

Time for upstream and downstream $=\frac{Distance}{Upstreamspeed} + \frac{Distance}{Downstreamspeed}$

                                                          $2=\frac{2}{u}+\frac{2}{d}$

Here u is the upstream speed, d is the downstream speed. Already we know the value of d  from the equation(1).

                                                     ∴   $2=\frac{2}{u}+\frac{2}{2+u}$

Take the L.C.M of $u$ and $2+u$  ⇒     $2=\frac{2(2+u)+2(u)}{u(2+u)}$

Take the common value of $2$ on both sides. That is,                                                          

                                                           $2=\frac{2[(2+u)+(u)]}{u(2+u)}$

Cancel $2$ on both sides. So that,       $1=\frac{2+u+u}{2u+u^2}$      

Do the cross multiplication ⇒ $2u+u^2=2+u+u$        

                                                 $2u+u^2=2+2u$    

                                         $2u+u^2-2u=2$      

                                                         $u^2=2$    

                                                           $u=\sqrt{2}$
                              Upstream speed $u=1.414kmph$