Advertisements
Advertisements
प्रश्न
A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?
उत्तर
Let x be the first speed of the train.
We know that `t=3 hours` Thus,we have,
`54/x+63/(x+6)=3 hours`
`54(x+6)+63x/(x(x+6))=3`
`54(x+6)+63x=3(x(x+6))`
`54x+324+63x=3x^2+18x`
`117x+324=3x^2+18x`
`3x^2-117x-324+18x=0`
`3x^2-99x-324=0`
`x^3-33x-108=0`
`x(x-36)+3(x-36)=0`
`(x+3)(x-36)=0`
`(x+3)=0 or (x-36)=0`
`x=-3 " or " x=36`
Speed cannot be negative and hence intial speed of the train is 36 km/hour.
APPEARS IN
संबंधित प्रश्न
A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.
A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?
Solve the following system of equations by cross-multiplications method.
`a(x + y) + b (x – y) = a^2 – ab + b^2`
`a(x + y) – b (x – y) = a^2 + ab + b^2`
Solve each of the following systems of equations by the method of cross-multiplication
2x − y = 6
x − y = 2
Solve each of the following systems of equations by the method of cross-multiplication
`(x + y)/(xy) = 2`
`(x - y)/(xy) = 6`
Solve each of the following systems of equations by the method of cross-multiplication
`x/a + y/b = 2`
`ax - by = a^2 - b^2`
Solve each of the following systems of equations by the method of cross-multiplication :
`ax + by = (a + b)/2`
3x + 5y = 4
The number of solutions of 3x + y = 243 and 243x - y = 3 is ______.
Solve the following pair of equations:
`1/(2x) - 1/y = -1, 1/x + 1/(2y) = 8, x, y ≠ 0`
A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.
