Respuesta :
Answer: U = 600 m/s
Step-by-step explanation:
Given that an aeroplane covers a distance of 1500km in a certain time t at a certain speed U.
After increasing the speed by 100km/hr, that is, V = U + 100 it covers the same distance in a time which is half an hour less than the previous time. That is t2 = t - 0.5.
From the first statement
Speed = distance/ time
Distance = speed × time
1500 = Ut
Make t the subject of the formula
t = 1500/U ..... (1)
From the second statement
Distance = speed × time
1500 = (U + 100) × ( t - 0.5 )
Open the bracket
1500 = Ut - 0.5U + 100t - 50
Collect the like terms
1550 = Ut - 0.5U + 100t .... (2)
Substitutes equation 1 into 2
1550 = 1500U/U - 0.5U + 100(1500/U)
1550 = 1500 - 0.5U + 150000/U
1550 - 1500 = (150000 - 0.5U^2)/U
Cross multiply
50U = 150000 - 0.5U^2
0.5U^2 + 50U - 150000 = 0
Divide all by 0.5
U^2 + 100U - 300000 = 0
Using completing the square method
U^2 + 100U = 300000
U^2 + 100U + 50^2 = 300000 + 50^2
(U + 50)^2 = 302500
U + 50 = sqrt(302500)
U + 50 = +/-(550)
U = 50 + 550 or 50 - 550
U = 600 or - 500
Since U is of the same direction, it is
positive. Therefore, the previous speed of the aeroplane is 600 m/s
Answer:
500km/hr
Step-by-step explanation:
The formula for Speed (km/hr) = Distance / Time
Where S = Speed
D = Distance
T = Time
S = D/T
From the question, the aeroplane covered a distance of 1500 km
S = 1500/ T
ST = 1500
Time taken( T ) = 1500/S ......... Equation 1
We are told from the question that speed was increases by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time
This is expressed mathematically as:
The new speed =S + 100km/hr
The new Time taken = 1500/ S - 1/2....... Equation 2
Also since Time = Distance / Speed
The new Time taken also = 1500/ S + 100 ......... Equation 3
Step 1
We would simplify Equation 2:
Time = 1500/S - 1/2
Find the Lowest common multiple = 2
Time = (2 × 1500 - S )/ 2S
Time = 3000 - S / 2S ......... Equation 4
Step 2
Equate Equation 4 and 3 together since they are both equal to time taken
1500/ S + 100 = 3000 - S / 2S
We cross multiply
2S × 1500 = (S + 100) ( 3000 - S)
3000S = 3000S - S² + 300000 - 100S
3000S - 3000S + S² - 300000 + 100S = 0
S² + 100S - 300000 = 0
Step 3
We solve for S = Speed by using factorisation method.
S² + 100x - 300000 = 0
S² - 500S + 600S - 300000 = 0
(S² - 500S) + (600S - 300000) = 0
S(S - 500) + 600(S - 500) = 0
(S - 500) (S + 600) = 0
S - 500 = 0, S = 500
S + 600 = 0 , S = -600
Our answer cannot be in negative form, hence, the previous speed of the aeroplane = 500km/hr
