How do i do this problem?
Suppose that car A travels 250 miles in 3 hours less time than it takes car
B to travel 440 miles. The rate of car B is 5 miles per hour faster than that
of car A. Find the rate of both cars.
2007-07-26 01:11:59 · 4 answers · asked by Tazzzy 1 in Science & Mathematics ➔ Mathematics
Let the rate of car A be x mph.
Then the rate of car B is x + 5 mph.
A travels 250 miles in 250 / x hr.
B travels 440 miles in 440 / (x + 5) hr.
250 / x = 440 / (x + 5) - 3
Multiplying by x(x + 5):
250(x + 5) = 440x - 3x(x + 5)
250x + 1250 = 440x - 3x^2 - 15x
3x^2 - 175x + 1250 = 0
(x - 50)(3x - 25) = 0
x = 50 or x = 25/3
The rates are A: 50 mph and B: 55 mph,
or A: 25/3 mph and B: 40/3 mph.
2007-07-26 01:25:45 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Car A travels 250 miles in time t
t = T - 3 where T is the time taken for B to travel 440 miles
Speed of car B is 5 mph more than speed of car A
Let s be the speed of car A and S that of car B
s = S - 5
T = 440/S
t = 250/(S - 5) = T - 3
440/S = 3 + 250 / (S - 5)
440 (S - 5) = 3S (S - 5) + 250 S
440S - 2200 = 3S^2 - 15S + 250S
3S^2 - 15S + 250S - 440S + 2200 = 0
3S^2 - 205S + 2200 = 0
This is a quadratic in S and can be solved. Once S is known, s can be derived by subtracting 5mph from S.
2007-07-26 08:25:01 · answer #2 · answered by Swamy 7 · 0⤊ 0⤋
rate B = rate A + 5
Time A = Time B - 3 . . . . since time = distance / rate
250 / A = 440 / B - 3 . . . . substitute B = A + 5
250 / A = 440 / (A+5) - 3
250 / A = (440 - 3 A - 15 ) / (A +5 )
250 (A + 5) = A (425 - 3A)
250 A + 1250 = 425 A - 3 A^2
3 A^2 175 A +1250 = 0
A = 50 & 8.3333
B = 55 & 13.333
2007-07-26 08:30:50 · answer #3 · answered by CPUcate 6 · 0⤊ 0⤋
call nasa
2007-07-26 08:15:45 · answer #4 · answered by Anonymous · 0⤊ 2⤋