a bmw travels 280 miles averaging at a certain speed. if the car gone 5 miles per hour faster, the trip would have taken 1 hour less. what is the average speed for the bmw?

Answer 1

We have two different trips with different speed and time in each case but the distance is the same which is 280 miles, so we will set up a system of two linear equations in speed(r) and time(t) using the equation d = rt, then solve the system of equations by the substitution method.

280 = rt ————> equation 1

280 = (r + 5)(t – 1) ————> equation 2

from equation 1 we can get t in terms of r by dividing both sides by r:

t = 280/r

now substitute for t in equation 2:

280 = (r + 5)(280/r – 1)

now lets simplify the the right side of the equation by multiplying the two binomials using the foil method:

280 = 280 – r + 1400/r – 5

let’s subtract 280 from both side

0 = – r + 1400/r – 5

now multiply by – r :

0 = r² – 1400 + 5r

now let’s but the quadratic equation in standard form:

r² + 5r – 1400 = 0

let’s solve the quadratic equation by factoring:

(r – 35)(r + 40) = 0

r – 35 = 0 or r + 40 = 0

r = 35 or r = –40 ( speed cannot be negative)

so r = 35 miles per hour

Answer 2

Let the speeds be x and x+5

Distance = (Rate)(Time), so Time = Distance/Rate

Time at slower speed = Time at faster speed + 1

280/x = 280/(x+5) + 1

280(x+5) = 280x + x(x+5)

280x + 1400 = 280x + x² + 5x

x² + 5x - 1400 = 0

(x+40)(x-35) = 0

So, x = 35 or -40.

Since x can't be negative, x = 35 mph.