mr kumar lives in the eastern part of spore . he visits his aged parents , who lives 36 km away , every weekend he finds that is he increases the average speed of his vehicle by 12km/h, he could save 9 minutes of his travelling time. find the speed at which he travels before the increase in speed
speed before increase : x km/h
time for trip with old speed = 36/x hrs
speed after increase : x+12 km/h
time for trip after increase = 36/(x+12)
36/x - 36/(x+12) = 9/60 = 3/20
divide by 3
12/x - 12/(x+12) = 1/20
multiply be 20x(x+12)
240(x+12) - 240x = x(x+12)
240x + 2880 - 240x = x^2 + 12x
x^2 + 12x - 2880 = 0
x^2 + 12 + 36 = 2880 + 36
(x+6)^2 = 2916
x+6 = ± √2916 = ±54
x = -6 ± 54
x = 48 or a negative
So he originally travelled at 48 km/h
check:
first time = 36/48= .75 hrs = 45 minutes
second time = 36/60 = .6 hrs = 36 minutes,
sure enough, the difference he gains is 9 minutes.
To find the speed at which Mr. Kumar travels before the increase in speed, we can use the formula:
Speed = Distance / Time
Let's denote Mr. Kumar's original speed as "x" km/h.
Given that the distance between his home and his parents is 36 km, we can calculate the time it takes for him to travel that distance at his original speed by rearranging the formula:
Time = Distance / Speed
So, the original time taken is 36 km / x km/h = 36/x hours.
If Mr. Kumar increases his average speed by 12 km/h, his new speed would be (x + 12) km/h.
Given that he saves 9 minutes of travel time, we need to convert the time difference into hours:
9 minutes = 9/60 = 0.15 hours
The new time taken at the increased speed is 36 km / (x + 12) km/h = 36/(x+12) hours.
According to the problem, the new time taken is 9 minutes (0.15 hours) less than the original time taken:
36/x - 0.15 = 36/(x+12)
To solve this equation, we can multiply the entire equation by x(x+12) to eliminate the denominators:
36(x+12) - 0.15x(x+12) = 36x
Expanding and simplifying the equation:
36x + 432 - 0.15x^2 - 1.8x = 36x
Rearranging and combining like terms:
0.15x^2 + 1.8x - 432 = 0
Now, we have a quadratic equation. We can solve it using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 0.15, b = 1.8, and c = -432.
Using the quadratic formula, we can solve for x.