Question

a motorboat whose speed is 18 km per hour in still water takes one hour more to go 24 km upstream then the return downstream to the same. Find the speed of the stream.

Answer 1

9Answer:

5 km/hr

Explanation:

As the speed of the boat in still water is known to us we can calculate the speed of the stream either any stream i.e. down stream or up stream.
Say, the speed of the stream is x km/hr.
Going downstream the speed of the boat and the speed of the stream will be added together i. e.(35+x) km/hr
Hence the boat goes (35+x) km in 1 hr.
For a distance of 60 km, the Time =6035+xhr
so, 6035+x=112=32
or, 3(35+x)=2⋅60 [cross multiplication]
or, 105+3x=120
or 3x=120−105
or, x=153=5
Speed of the stream is 5 km/hr.
Another way
Going upstream, the speed of the stream is deducted from speed of the boat i.e (35−x)km/hr
Hence goes (35−x) km in 1 hr.
Therefore for a distance of 60 km Time = 6035−xhrs.
As per question, Time is 2 hours, so 6035−x=2
or 60=2(35−x) [ cross multiplication]
or, 60=70−2x
or 2x=70−60
or, x=102=5
So, speed of the stream is 5 km/hr.

Answer 2

Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

24/(18 - x) = 1 + 24/(18 + x)

24/(18 - x) - 24/(18 + x) = 1

x2 + 48x - 324 = 0

(x + 54)(x - 6) = 0

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream = 6 km/hr