A motorboat goes down stream in a river
and covers the distance between two
coastal towns in five hours. It covers
this distance upstream in six hours. If
the speed of the stream is 2 km/hour
find the speed of the boat in still water.
Answers
Answer:
Since we have to find the speed of the boat in still water, let us suppose that it is x km/h.
This means that while going downstream the speed of the boat will be (x+2) kmph because the water current is pushing the boat at 2 kmph in addition to its own speed 'x' kmph.
Now the speed of the boat down stream =(x+2) kmph
⇒ distance covered in 1 hour =x+2 km
∴ distance covered in 5 hours =5(x+2) km
Hence the distance between A and B is 5(x+2)km
But while going upstream the boat has to work against the water current.
Therefore its speed upstream will be (x−2) kmph.
⇒ Distance covered in 1 hour =(x−2) km
Distance covered in 6 hours =6(x−2) km
∴ distance between A and B is 6(x−2) km
But the distance between A and B is fixed
∴ 5(x+2)=6(x−2)
⇒ 5x+10=−12−10
∴ −x=−22
x=22
Therefore speed of the boat in still water is 22 kmph.
Hope, it helps.... :)
Answer:
Boats and streams is one of the most common topics in quantitative section of all the entrance exams such as Bank PO, CAT, XAT, CLAT etc. It’s also included in aptitude section of many job test in companies like TCS, Infosys etc. This a very simple topic and mere require direct application of formulas to solve the question. However, many students find this topic confusing and find face difficulties in solving them. And, the reason for facing such hindrance is the understanding of the language of question. They are just Speed, Distance and Time questions in water rather with a slightly twisted language. In this blog, today I will provide you all the formulas and their application to make understand this concept and application so that the next time you get any question based on this topic in any exam it’s a smooth ride!
Let’s begin!
First, I’ll explain you the few terms that you will generally find in all the questions and type of question that can come in exam.
Upstream: It means that you are moving in opposite direction from that in which river flows.
Downstream: It means moving along in the direction of the flow of the stream.
Let the speed of boat be a km/hr. and speed of the stream be b km/ hr. Therefore, the relative speed of boat going upstream is (a-b) km/hr. and speed of the boat going downstream will be (a + b) km/hr.
Still water: When the water is still and not moving and there’s no flow like that in case of ponds then it’s called still water.
Then, the relative speed of boat in still water is ½ (a + b) km/hr. And, the speed of stream is ½ (a – b) km/hr.
Some basic types of questions asked in exam
Time based questions
Speed based questions
Average speed-based questions
Distance based questions
Now let’s learn some problem-solving in above mentioned questions:
Time based question: In this kind, you will be given speed of the boat and stream in still water. You need to calculate the time to go upstream/ downstream. There can also be other questions in calculation of time and some of them can be easily be solved using the formulas given below.
Example 1: The speed of a motor boat is that of the stream as 36:5. The boat goes along with the stream in 5 hours and 10 minutes. How much time will it take to come back?
Sol) Let the speed of the motor boat and that of stream be 36x km/hr. and 5km/hr. respectively.
Then, the speed downstream = (36x + 5x) = 41km/hr.
Speed upstream = (36x – 5x) = 31 km/hr.
Let d the distance.
Then, d/41 km = 5 10/60 = 31/6
d = 1271x/6
Time taken while coming back = distance/speed = d/31x = 1271x/ (31x * 6) hrs. = 6 5/6
Speed based question: In this kind, you will be given speed of boat upstream and downstream, you need to find the speed of still water and stream.
Step-by-step explanation:
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