A boat covers a certain distance downstream in 3 hours and the same distance upstream in 5 hours. If the speed of the boat in still water is 8 km/hr , Find the speed of the stream.
chapter - Linear Equation in one variable.
Plz explain this clearly briefly
I don't know the answer plz help me , weak in mathematics.
Answers
Answer:
Explanation : speed of boat in still water is 8 kmph. Means, where there is no movement in water (like in pond, lake), the boat coveres distance of 8 km in one hour. Imagine when the boat will row in a river, there will certainly be effect of flow of river on the speed of the boat. , boat will generate its own same speed in river also, but for an observer outside river and still on ground, the effective speed of boat. will appear different.. You can best understand this by imagining a moving floor like in airports. imagine your friend is standing on ground beside moving floor and you are standing on a moving floor. The floor is moving at a speed of say 3 kmph. Now, even if you are not moving on your own, your friend will feel that you are moving at a speed of 3 kmph. Now imagine that in order to talk to your friend you start walking in direction opposite to movement of floor so that distance between you and your friend is not changing. To your friend, your speed is zero because your position is not changing w.r.t your friend but in actual you are walking at a speed of 3 kmph in opposite direction. The resultant zero speed is due to calculation of net speed for a stationary observer. Hence your net spped in this case was (3 - 3) kmph. Again, imagine you start walking on the moving floor at a speed of 2 kmph in the same direction of movement of floor so that you may pass standing persons on floor. your speed for a person on floor will be 2 kmph but for your friend on ground i.e. a stationary observer you speed will be more than 2 kmph. How much more? Exactly, 3 kmph more and your resultant speed will be (3+2) kmph.
Now back to problem:
speed of boat in still water = 8 kmph
let speed of stream be x kmph
effective speed downstream (means in the direction of stream) = (8 + x) kmph.
effective speed upstream. (in opposite direction of stream) = 8 - x (speed of boat is more)
time taken downstream = 3 hours.
distance = speed*time
= (8+x)*3
= 3x + 24
time taken upstream = 5 hours
distance = speed x time
= (8-x)*5
= 40 - 5x
but the distance is same, hence
3x + 24 = 40 - 5x
3x + 5x = 40 - 24
2x = 16
x = 8 kmph
hope I was able to explain in a lucid way.