Advertisements
Advertisements
Question
A car made a run of 390 km in ‘x’ hours. If the speed had been 4 km/hour more, it would have taken 2 hours less for the journey. Find ‘x’.
Advertisements
Solution
Let the original speed of the car be y km/hr
We know
`"Speed" = "Distance"/"Time"`
∴ `y = 390/x`
`=> x = 390/y` ...(1)
New speed of the car = (y + 4) km/hr
New time taken by the car to cover 390 km = `390/(y + 4)`
From the given information,
`390/y - 390/(y + 4) = 2`
`(390y + 1560 - 390y)/(y(y + 4)) = 2`
`780/(y^2 + 4y) = 1`
y2 + 4y – 780 = 0
y2 + 30y – 26y – 780 = 0
y(y + 30) – 26(y + 30) = 0
(y + 30)(y – 26) = 0
y = –30, 26
Since, time cannot be negative, so y = 26
From (1), we have
`x = 390/y = 390/26 = 15`
RELATED QUESTIONS
The sides of a right-angled triangle containing the right angle are 4x cm and (2x – 1) cm. If the area of the triangle is 30 cm2; calculate the lengths of its sides.
The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.
The hypotenuse of a right-angled triangle exceeds one side by 1 cm and the other side by 18 cm; find the lengths of the sides of the triangle.
The perimeter of a rectangle is 104 m and its area is 640 m2. Find its length and breadth.
The dimensions of a rectangular field are 50 m and 40 m. A flower bed is prepared inside this field leaving a gravel path of uniform width all around the flower bed. The total cost of laying the flower bed and gravelling the path at Rs. 30 and Rs. 20 per square metre, respectively, is Rs. 52,000. Find the width of the gravel path.
An area is paved with square tiles of a certain size and the number required is 128. If the tiles had been 2 cm smaller each way, 200 tiles would have been needed to pave the same area. Find the size of the larger tiles.
The area of a big rectangular room is 300 m2. If the length were decreased by 5 m and the breadth increased by 5 m; the area would be unaltered. Find the length of the room.
The perimeter of a rectangular field is 28 m and its area is 40 sq. m. Its sides are ______.
In the given figure, the value of x is ______.
The area of the given rectangle is 60 sq. m and its longer side is 10 m, the perimeter of the rectangle is ______.
