Question

 A boat takes 64 minutes less to travel 40 km downstream then to travel the same distance upstream if the speed of the boat in Stillwater is 20 km/h then the speed of the stream is___

Answer 1

Answer:

Let the speed of Stream be y km/h then

Let the time taken to go 40 km downstream be t hours

then the time taken to go 40 km upstream is (t+1) hours .........since 60 min=1 hr

Also,

time = distance/ speed

so,

t=40/(15+y)

t+1=40/(15-y)

Now,

=>40/(15-y) - 40/(15+y) = 1

=> y²+80y - 225 =0;

we get,

y= 2.72 km/h

so the speed of the stream is 2.72 km/h

Answer 2

Given :

Speed of boat in stillwater = 20km/h

Distance travelled by the boat both upstream and downstream= 40 km each

To find : Speed of the stream

Solution :

Let the speed of the stream be v km/hr

Therefore,Speed of the boat downstream = (20 + v) km/hr

Speed of the boat upstream = (20 - v) km/hr

We know that

Time = distance/speed

Time upstream t1 = 40/(20 - v)

Time downstream t2 = 40/(20 + v)

t1 - t2 = 40/(20 - v) - 40/(20 + v)

= 40[1/(20 - v) - 1/(20 + v)]

= 40[2v/(20 - v)(20 + v)]

= 80v/(20 - v)(20 + v) = 80v/(400 - v²)

According to the question,

t1- t2 = 64 minutes = 64/60 hr

Hence, 80v/(400 - v²) = 64/60

80v × 60 = 64(400 - v²)

600v = 8(400 - v²)

8v² + 600v - 3200 = 0

V² + 75v - 400 = 0

Solving, we get v = 5, v = -80

Since Speed cannot be negative, therefore v = 5

Hence, speed of the stream = 5 km/hr

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