Advertisements
Advertisements
प्रश्न
The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction?
Advertisements
उत्तर
Let the ongoing speed of person be x km/hr. Then,
Returning speed of the person is = (x + 10)km/hr.
Time taken by the person in going direction to cover 150km = `150/x`hr
Time taken by the person in returning direction to cover 150km = `150/(x+10)`hr
Therefore,
`150/x-150/(x+10)=5/2`
`(150(x+10)-150x)/(x(x+10))=5/2`
`(150x+1500-150x)/(x^2+10x)=5/2`
`1500/(x^2+10)=5/2`
1500(2)=5(x2+10x)
3000 = 5x2 + 50x
5x2 + 50x - 3000 = 0
5(x2 + 10x - 600) = 0
x2 + 10x - 600 = 0
x2 - 20x + 30x - 600 = 0
x(x - 20) + 30(x - 20) = 0
(x - 20)(x + 30) = 0
So, either
x - 20 = 0
x = 20
Or
x + 30 = 0
x = -30
But, the speed of the train can never be negative.
Thus, when x = 20 then
= x + 10
= 20 + 10
= 30
Hence, ongoing speed of person is x = 20 km/hr
and returning speed of the person is x = 30 km/hr respectively.
APPEARS IN
संबंधित प्रश्न
Solve for x
`(2x)/(x-3)+1/(2x+3)+(3x+9)/((x-3)(2x+3)) = 0, x!=3,`
Solve the following quadratic equation by factorization method : `3x^2-29x+40=0`
Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?
The sum of two natural numbers is 9 and the sum of their reciprocals is `1/2`. Find the numbers .
Solve the following quadratic equation by factorization.
`2"x"^2 - 2"x" + 1/2 = 0`
Solve the following quadratic equations by factorization:
\[9 x^2 - 6 b^2 x - \left( a^4 - b^4 \right) = 0\]
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
Show that x = −2 is a solution of 3x2 + 13x + 14 = 0.
If ax2 + bx + c = 0 has equal roots, then c =
If p and q are the roots of the equation x2 – px + q = 0, then ______.
If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =
Solve the following equation: a2x2 - 3abx + 2b2 = 0
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
Solve the equation using the factorisation method:
`(3x -2)/(2x -3) = (3x - 8)/(x + 4)`
There are three consecutive positive integers such that the sum of the square of the first and the product of other two is 154. What are the integers?
Harish made a rectangular garden, with its length 5 metres more than its width. The next year, he increased the length by 3 metres and decreased the width by 2 metres. If the area of the second garden was 119 sq m, was the second garden larger or smaller ?
Solve the following equation by factorisation :
3x2 + 11x + 10 = 0
For equation `1/x + 1/(x - 5) = 3/10`; one value of x is ______.
