Advertisements
Advertisements
प्रश्न
Pratik takes 8 hours to travel 36 km downstream and return to the same spot. The speed of boat in still water is 12 km. per hour. Find the speed of water current.
उत्तर
Let the speed of water current = x km/h
Speed of boat in still water = 12 km/h
Speed upstream = (12 − x) km/h
Speed downstream = (12 + x) km/h
Distance travelled = 36 km downstream and 36 km upstream
Total time taken by Pratik = 8 hrs
`"Speed" = "Distance"/"Time"`
∵ `"Time" = "Distance"/"Speed"`
Time taken to travel 36 km downstream + time taken to travel 36 km Upstream = 8hrs
`⇒ 36/(12 + x) + 36/(12 - x) = 8`
`⇒ 36[1/(12 + x) + 1/(12 - x)] = 8`
`⇒ 9[((12 - x) + (12 + x))/((12 + x)(12 - x))] = 2`
`⇒ 9[(12 - x + 12 + x)/(144 - x^2)] = 2`
`⇒ 9 × 24/(144 - x^2) = 2`
`⇒ 9 × 24 = 2(144 - x^2) `
`⇒ (9 × 24)/2 = 144 - x^2 `
`⇒ 9 × 12 = 144 - x^2 `
`⇒ 108 = 144 - x^2 `
`⇒ x^2 = 144 - 108`
`=> 9 xx 24 = 2 (144 - x^2)`
`=> 9 xx 12 = 144 - x^2`
`=> 144 - 108 = - x^2`
`=> x^2 = 36`
`=> x = +- 6` , but speed ≠ negative
so , x = 6 km/h
Hence, speed of water current is 6 km/h
APPEARS IN
संबंधित प्रश्न
If the sum of the roots of the equation `kx^2+2x+3k=0` is equal to their product then the value of k
`(a) 1/3 (b)-1/3 (c)2/3 (d)-2/3`
If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is
(a)`x^2-6x+6=0` (b)` x^2+6x+6=0` (c)`x^2-6x-6=0` (d)`x^2+6x+6=0`
If the roots of the equation` ax^2+bx+c=0` are equal then c=?
(a)`b/(2a)` (b) `b/(2a)` (c) `-b^2/(4a)` (d) `B^2/(4a)`
The roots of `ax^2+bx+c=0`,a≠0 are real and unequal, if `(b^2-4ac)` is
(a)>0 (b)=0 (c)<0 (d)none of these
The roots of the equation 2x^2-6x+7=0 are
(a) real, unequal and rational (b) real, unequal and irrational (c) real and equal (d) imaginary
The length of a rectangular field exceeds its breadth by 8 m and the area of the field is `240 m^2` . The breadth of the field is
(a) 20 m (b) 30 m (c) 12 m (d) 16 m
If the quadratic equation `px^2-2sqrt5px+15=0` has two equal roots then find the value of p.
Find the value of k for which the quadratic equation `9x^2-3kx+k=0` has equal roots.
Solve` 2x^2+ax-a^2=0`
Solve `sqrt3x^2+10x-8sqrt3=0`
If 1 is a root of the equations ay2 + ay + 3 = 0 and y2 + y + b = 0 then ab equals: ?
Suyash scored 10 marks more in second test than that in the first. 5 times the score of the second test is the same as square of the score in the first test. Find his score in the first test.
Pintu takes 6 days more than those of Nishu to complete certain work. If they work together they finish it in 4 days. How many days would it take to complete the work if they work alone.
Choose the correct answer for the following question.
Out of the following equations, find the equation having the sum of its roots –5.
If 3x + 5y = 9 and 5x + 3y = 7 find the value of x + y.
For the quadratic equation x2 + 10x – 7 = 0, the value of a, b, c are ______.
Obtain a quadratic equation whose roots are –3 and –7.
Two water taps together can fill a tank in `1(7)/(8)` hours. The tap with longer diameter takes 2 hours less than the tap with a smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.
If 460 is divided by a natural number, then quotient is 2 more than nine times the divisor and remainder is 5. Find the quotient and divisor.
