Question

A man rows a boat at a speed of 5 km/hr in still water. find the speed of a river if it takes him 1 hr to row a boat to a place 2.4 km away and return back.

Answer 1

To calculate this question, we will assume that the speed of the river is x km/hr

Here are some speed time formulas we will use: 

Speed = distance / time

Time = distance/ speed

Total distance he covers: 

2.4 km + 2.4 km = 4.8 km

The speed he uses away ( assuming its downstreamstream)

5km/hr + x km/hr = (5+x) km/hr

Therefore time taken to go downstream will be :

Time  = distance/speed = 2.4km/(x+5)km/r

The speed he uses to return ( assuming its  upstream)

5-x km/hr

Time taken coming back:

Time = distance / speed = 2.4 km / 5-x km/hr

The total time taken way and back therefore is:

2.4/x+5 + 2.4/5-x = (2.4x -12)+ (2.4x +12) /(x+5)(5-x) = 4.8x/(x+5)(5-x)


Therefore :

4.8x/(x+5)(5-x) = 1 hr ( time taken going and coming back)

Hence: When you cross multiply;

4.8x = (x+5)(5-x)

x(5-x) +5(5-x) = 4.8x

5x - x² + 25 - 5x = 4.8x

-x² +25 = 4.8x

x² -25= -4.8x

x² + 4.8x - 25= 0

(x - 3.14617)(x+7.94617)

x = 3.14617 or - 7.94617

Since the speed of the river cannot be a negative number,

Therefore the speed of the river is 3.14617km/hr

Answer 2

Let the speed of river be x.

Then, Speed downstream = (5 + x) kmph

Speed upstream = (5 - x) kmph

Then,

=> 2.4/(5+x) + 2.4/(5-x) = 1

=> 2.4(10) = 5^2 - x^2

=> x^2 = -1

=> x = 1 km/hr