A jet flew from Tokyo to Bangkok, a distance of 4800km. On the return trip the speed was decreased by 200km/h. If the difference times of the fights was 2 hours, what was the speed from Bangkok to Tokyo.
time for 1st flight = 4800/x
time for return flight = 4800/(x-200)
4800/(x-200) - 4800/x = 2
multiply by x(x-200)
4800x - 4800(x-200) = 2x(x-200)
960000 = 2x^2 - 400x
x^2 - 200x - 480000=0
(x - 800)(x + 600) = 0
x = 800 or x = -600 , the negative speed makes no sense
so x = 800 km/h
check:
1st flight = 4800/800 = 6 hrs
2nd flight = 4800/600 = 8 hrs
difference is 2 hours, YEahh!
Let's denote the speed of the jet from Tokyo to Bangkok as 'x' km/h.
On the return trip, the speed is decreased by 200 km/h, so the speed from Bangkok to Tokyo can be represented as 'x - 200' km/h.
The time it takes to fly from Tokyo to Bangkok is given by the formula: time = distance / speed. So the time for the Tokyo to Bangkok flight is 4800 / x hours.
According to the given information, the difference in times for the two flights is 2 hours. Therefore, we can set up the equation:
4800 / x - 4800 / (x - 200) = 2
To solve this equation, we can eliminate the denominators by multiplying both sides by x(x-200):
4800(x-200) - 4800x = 2x(x-200)
Expanding and simplifying:
4800x - 960000 - 4800x = 2x^2 - 400x
Rearranging and simplifying further:
2x^2 - 400x - 960000 = 0
Dividing the entire equation by 2:
x^2 - 200x - 480000 = 0
Now we can solve this quadratic equation using factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 1, b = -200, and c = -480000:
x = (-(-200) ± √((-200)^2 - 4*1*(-480000))) / (2*1)
Simplifying:
x = (200 ± √(40000 + 1920000)) / 2
x = (200 ± √(1960000)) / 2
x = (200 ± 1400) / 2
Now we have two possible values for x:
x1 = (200 + 1400) / 2 = 1600 / 2 = 800 km/h
x2 = (200 - 1400) / 2 = -1200 / 2 = -600 km/h
Since the speed of the jet cannot be negative, we can conclude that the speed from Bangkok to Tokyo is 800 km/h.
To find the speed from Bangkok to Tokyo, we can set up a system of equations using the given information.
Let's assume the speed of the jet from Tokyo to Bangkok is "x" km/h.
Therefore, the speed of the jet from Bangkok to Tokyo (with a decreased speed) would be "x - 200" km/h.
We know that the distance from Tokyo to Bangkok is 4800 km and that the time difference between the flights is 2 hours.
Using the formula: Speed = Distance / Time, we can write two equations:
1) x = 4800 / (time from Tokyo to Bangkok)
2) x - 200 = 4800 / (time from Bangkok to Tokyo)
Since the difference in time is 2 hours, we can express the time from Bangkok to Tokyo as the time from Tokyo to Bangkok + 2:
x - 200 = 4800 / (x + 2)
Now we can solve this equation to find the value of "x" (the speed from Bangkok to Tokyo).
Multiply both sides of the equation by x + 2:
(x - 200)(x + 2) = 4800
Expand the left side of the equation:
x^2 + 2x - 200x - 400 = 4800
Combining like terms:
x^2 - 198x - 5200 = 4800
Rearrange the equation:
x^2 - 198x - 10000 = 0
Now we have a quadratic equation. We can solve it using quadratic formula or by factoring. However, this equation doesn't factor easily, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, the values of a, b, and c can be identified as follows:
a = 1, b = -198, c = -10000
Plugging the values into the quadratic formula:
x = (-(-198) ± √((-198)^2 - 4(1)(-10000))) / (2(1))
Simplifying the equation:
x = (198 ± √(39204 + 40000)) / 2
x = (198 ± √(79204)) / 2
x = (198 ± 281.15) / 2
Using both the positive and negative values:
x₁ = (198 + 281.15) / 2 = 479.58 km/h
x₂ = (198 - 281.15) / 2 = -41.58 km/h
Since speed cannot be negative, the speed from Bangkok to Tokyo would be approximately 479.58 km/h.