Speed of boat in still water
=| Downstreamspeed + Upstreamspeed |
| 2 |
Downstream speed = Speed of boat in still water + Speed of the stream
Upstream speed
= Speed of boat in still water - Speed of the stream
Calculation:
Let the speed of the boat in still water be
xkm∕h.
Downstream speed
=x+9km∕hUpstream speed
=x−9km∕hTime taken to travel downstream
=56∕(x+9)Time taken to travel upstream
=28 / (
x−9 )
Total time
=7 hours
⇒56∕(x+9)+28∕(x−9)=7Multiply both sides by
(x+9)(x−9) :
⇒56(x−9)+28(x+9)=7(x+9)(x−9)⇒56x−504+28x+252=7(x2−81)⇒84x−252=7x2−567Rearrange the equation:
⇒7x2−84x−315=0Divide the entire equation by 7 :
⇒x2−12x−45=0 Factorize the quadratic equation:
⇒(x−15)(x+3)=0⇒x=15 or x=−3Since speed cannot be negative,
x=15km∕h.