  Question: It takes 4 hours for a person to travel 15 km in favor of current and 3 km against current. Again it takes 9 hours to go 20 km in favor of the current and 15 km against the current How many km per hour speed of the boat in still water?

Posted by: Surajit P. on 24.05.2022  • Like

Let the speed of the boat in still water =  x km/hr

Let the speed of the current  =   y km/hr

Then the speed of the boat down stream (in favour of current) =  x+y  = u (say)

Speed of the boat in upstream(against  the  current)   =   x-y  =  v(say)

The distance traveled by the boat in downstream = 15 km

Time taken in downstream travel  =  15/u

The distance traveled in upstream = 3km

Time taken in upstream travel =  3/v

Total time of travel in the boat =  (15/u) +(3/v) = 4 hrs(given)  ……….        A

In the second instance  distance  traveled in downstream = 20kms

Time taken in downstream travel  =   20/u

Distance traveled in upstream   =  15 kms

Time taken in upstream travel =  15/v

Total time of travel in boat =  (20/u)+(15/v)   = 9 hrs (given)   …………      B

We have        (15/u)  +  (3/v)   =     4

(20/u)+ (15/v)   =      9  or (4/u) +(3/v) =  9/5

Eliminating v ,we get  11/u  =   11/5 .Therefore u =5

Now putting this value in “A”, we get (15/5) + (3/v ) =  4  or

3/v = 4-3 =  1 .Therefore  v =  3

Thus we have two new equations as below:

u= x+y =    5

v= x-y  =    3

Eliminating y ,we get 2x =  8 or  x =4

Hence the speed of the boat in still waters =x = 4 km/nr. Sultan S. from Chandigarh
• Like
Https://youtu.be/HN4cwuCbUlA Mukesh S. from Meerut
• Like
This question is based on speed , time and distance as well as formation of linear equations in two variables. Similar Questions
Topic Cloud

## Need a Tutor or Coaching Class?

Post an enquiry and get instant responses from qualified and experienced tutors.

Post Requirement

Drop Us a Query