Advertisements
Advertisements
Question
The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Advertisements
Solution
Let the speed of the stream be x km/hr.
∴ Speed of the boat downstream = (15 + x) km/hr
Speed of the boat upstream = (15 – x) km/hr
Time taken to go 30 km downstream = `30/(15 + x)` hr
Time taken to come back = `30/(15 - x)` hr
From the given information,
`30/(15 + x) + 30/(15 - x) = 4 30/60`
`30/(15 + x) + 30/(15 - x) = 9/2`
`(450 - 30x + 450 + 30x)/((15 + x)(15 - x)) = 9/2`
`900/(225 - x^2) = 9/2`
`100/(225 - x^2) = 1/2`
225 – x2 = 200
x2 = 25
x = ±5
But, x cannot be negative, so, x = 5.
Thus, the speed of the stream is 5 km/hr.
APPEARS IN
RELATED QUESTIONS
The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages.
The sum S of n successive odd numbers starting from 3 is given by the relation: S = n(n + 2). Determine n, if the sum is 168.
The age of a father is twice the square of the age of his son. Eight years hence, the age of the father will be 4 years more than three times the age of the son. Find their present ages.
Mr. Mehra sends his servant to the market to buy oranges worth Rs. 15. The servant having eaten three oranges on the way, Mr. Mehra pays Rs. 25 paise per orange more than the market price. Taking x to be the number of oranges which Mr. Mehra receives, form a quadratic equation in x. Hence, find the value of x.
Rs. 250 is divided equally among a certain number of children. If there were 25 children more, each would have received 50 paise less. Find the number of children.
The total cost price of a certain number of identical articles is Rs. 4800. By selling the articles at Rs. 100 each, a profit equal to the cost price of 15 articles is made. Find the number of articles bought.
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from the numerator and the denominator both, the fraction reduces by `1/14`. Find the fraction.
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.
Rs. 480 is divided equally among ‘x’ children. If the number of children were 20 more, then each would have got Rs. 12 less. Find ‘x’.
Two years ago the ages of Radha and Meena were in the ratio 5 : 2. If the sum of their present ages is 39 years, their ages, 2 years ago, were ______.
