Merrily Down The Stream

We have been given that sped of boat in still water is 9 mph. The distance is 12 miles.The speed of stream is 3 mph.

So we know Avg Speed = Total distance/Total time

Total trip distance is 24 miles.

Speed of boat with up stream is (Speed in still water - Speed of stream)

(9mph - 3mph)= 6mph

* Time = 12miles/ 6mph = 2 Hours *

Speed of boat with down stream is (Speed in still water + Speed of stream)

(9mph + 3mph)= 12mph

* Time = 12miles/ 12mph = 1 Hour *

So we now can compute Average Speed= 12miles + 12 miles/1 hour+ 2 hour

= 24/3

* = 8 miles per hour *

Averages and Mean are different.. i don't know exactly why but how it's work for average. You may think the answer is 9 but that is mean not average. i have seen question like this about average and mean. Here i tell you how mean works:

This data is speed of boat there and return:

1)(9-3)mil/hour=6mil/hour,

2)(9+3)mil/hour=12mil/hour

from those data find the average, if x=average speed and x/2=half of average speed(of data)

(x/2)(1/6)=x/12

(x/2)(1/12)=x/24

Then the average speed is x/12+x/24=0 then3x=24 and then x=8

Given that, Speed of boat in still water $=9$ miles/hr.

Now, while going upstream, the stream resists the velocity of the boat and so net velocity of the boat $=9-3=6$ miles/hr. So, Time to travel upstream $(t_1)=\frac{\text{Distance}}{\text{Speed}}=\frac{12}{6}=2$ hr.

Then, while going downstream, the stream adds its velocity to the boat and the boat moves with velocity $=9+3=12$ miles/hr. So, Time to travel downstream $(t_1)=\frac{\text{Distance}}{\text{Speed}}=\frac{12}{12}=1$ hr.

So, total distance travelled $(D)=12+12=24$ miles and time taken $(T)=2+1=3$ hr.

So, Average Speed during the journey $=\frac{D}{T}=\frac{24}{3}=\boxed{8\text{ miles/hr}}$

Total Time=12/6 +12/12=3; Total Distance=24; Average speed=24/3=8

For upstream speed of boat - speed of stream

For downstream speed of boat + speed of stream

For finding avg. speed when we compare 2 velocities & the distance traveled with both the velocities is same then avg.

 speed = 2 X a X b / a + b where a & b are velocities.

speed of boat upstream = 9-3=6 miles per hour

speed of boat downstream= 9 +3=12 miles per hour

time taken to travel upstream=distance/speed=12/6

time taken to travel downstream=distance /speed=12/12

average speed= total distance/total time=12+12/2+1=8 miles per hour

Along up stream speed per hour (9-3)or 6 miles and so it too (12/6)=2 hours time to reach the destination. Again along downstream speed per hour(9+3)or 12 miles and for that it took (12/12)or 1 hour time to return the place. Now total distance covered (12+12) or 24 miles and time taken (2+1) or 3 hours. So, average speed for the whole trip (24/3) or 8 miles per hour.

Quite Simple. Since the speed in still water is 9 mph, and stream is 3 mph. Downstream speed will be (9+3) = 12 and Upstream will be (9-3) = 6.

To cover 12 upstream it will take 2 hours and to cover 12 downstream it will take 1 hour. Total distance covered 24 and total time taken is 3 hours. 24/3 = 8 will be the average for the whole trip.

given the rate of stream = (a-b)/2=3 a-b=6------(1)eq,here a ,b are upstream and downstream, and a=12 substitute for b and get the value as b=6, wee know the average speed,s=(2 a b)/(a+b) we get the answer a 8

t1= 12/(9+3) time in downstream t2=12/(9-3) time in upstream

average speed =(12 upstream+12 downstream)/(t1+t2)=24/(1+2)=8

average speed is calculated by total distance and the total time taken to travel the distance it is given by the formula: total distance travelled/total time here we need to break the motion of the boat into two phases first - when it was going upstream: when the boat was going upstream, its velocity as seen from the ground would be velocity of boat-velocity of stream (as both are in opposite direction) so the velocity of the boat as seen from the ground will be 6mph so the time taken to move up the 12 miles distance=distance travelled/speed=12/6=2hours the second phase f the motion- when the boat goes downstream: when the boat goes downstream , its velocity as seen from the ground = velocity of boat+velocity of stream=12mph so the time taken o return back = total distance/speed=12/12=1 so , the total distance travelled=12+12=24 miles and the total time taken = 3hours so the average speed of the boat is =24/3=8miles per hour

Speed of the boat in still water is 9 miles/hr. When he is going upstream he is losing 3 miles/hr. So the speed of the boat upstream is 6 miles/hr. This means it will take the boat 2 hrs to travel the 12 miles.

Downstream, the boat will gain 3 miles/hr. So the speed of the boat will be 12 miles/hr. This means the boat will only take 1 hr to travel the 12 miles back.

Total travel miles is 12 upstream and 12 downstream. 12 + 12 = 24 miles. Total time taken is 2 hrs upstream and 1 hr downstream. 2 + 1 = 3 hrs.

Average time is distance divided by time. 24/3 = 8 miles/hr.

From the passage we know that the boat move 9 mile per hour and the stream move 3 mile per hour.

There must be 2 situation either the stream opposite the boat or vice versa.

n is for the hour, n(9-3)=12 and n(9+3)=12 n=2,1

so the total of hour for the boat to travel and return to origin is 2+1=3

lastly we need to devide the total path by the total time 24/3=8 mile per hour.

Speed of boat with up stream is (Speed in still water - Speed of stream) (9mph - 3mph)= 6mph * Time = 12miles/ 6mph = 2 Hours* Speed of boat with down stream is (Speed in still water + Speed of stream) (9mph + 3mph)= 12mph * Time = 12miles/ 12mph = 1 Hour* Total trip distance is 24 miles. Total Travel Time 3Hrs So Average Seed = 24/3 * = 8 miles per hour *

The question can be easily sovled even when the total distance to be covered is not given. I can show you how.

By definition:

Average Speed = Total Distance/Total time

Let distance be S and let upstream speed be u and downstream speed be v.

Now, Total Time(TT) = Upstream time+Downstream Time TT = S/u +S/v TT = S(1/u +1/v)

Now, Average Speed = 2S/Total time Average Speed = 2S/S(1/u +1/v)

On solving, Average Speed = 2vu/v+u

As you can see, this formula is independent of distance S.

Putting the values, you should get 8 as the answer.

upstream speed=3+9=12mph: downstream speed=9-3=6kmph time required for upstream journey=12/12 =1 hr: time required for downstream journey=12/6=2hr Avg speed= total dist /total time =24/3=8hr

Average speed = 2xy/(x+y)

So we know Avg Speed = Total distance/Total time

Total trip distance is 24 miles.

Speed of boat with up stream is (Speed in still water - Speed of stream)

(9mph - 3mph)= 6mph

Time = 12miles/ 6mph = 2 Hours

Speed of boat with down stream is (Speed in still water + Speed of stream)

(9mph + 3mph)= 12mph

Time = 12miles/ 12mph = 1 Hour

So we now can compute Average Speed= 12miles + 12 miles/1 hour+ 2 hour

= 24/3

= 8 mile per hour

AVERAGE SPEED = ((UPSTREAM RATE) * (DOWNSTREAM RATE)) / STILL WATER SPEED

=((9-3) * (9+3)) / 9 = 72/9 =8

since the speed of the steam is 3 miles /h and it resisted the boat while travelling upstream so the speed of the boat became 6 miles / h (9-3) and since the distance = 12 miles and (v=d/t) so time = d/v = 12/6 = 2 hours but while travellind down the speed became 12 miles / h as the boat and the stream in one direction and the time while travelling down is 12 / 12 = 1 hour so total time = 3 hours average speed = 24/3=8 miles / hour

for upstream: speed=(9-3)=6miles per hour, require time=12miles/6mph=2hours for downstream: speed=(9+3)=12miles per hour,require time=12miles/12mph =1hour total trip=24miles, total time=3hours avg speed of boat=24miles/3hours=8miles an hour

upstream travel----------> distance = 12, speed = 9 -3 = 6, therefore time(t1) = 12/6 = 2hr

downstream travel---------> distance = 12, speed = 9 +3 = 12, therefore time(t2) = 12/12 = 1hr

Average speed = total distance / total time = (12+12) /(t1+t2) = 24/3 = 8

(x+3) t1 =12 (x-3) t2 =12 X = speed of boat in still water =9 T1=time taken upstream T2=time taken downstream average speed = total distance (24)/t1+t2 t1=1 t2=21+t2=3 average speed =24/3 =8

channel speed: 3 miles/hr

upstream boat speed: 12 miles/hr

boat speed in still water: 9 miles/hr

hence, downstream speed: (9-3)=6 miles/hr

suppose boat travels 12miles upstream and comes back. it need 1hr to go (upstream speed 12miles/hr) and needs 2hrs to return(downstream speed 6miles/hr).

it took 3 hrs to cover 24 miles.

hence avg speed = 24/3=8miles/hrs