Santos went on a bike ride of 90 miles. He realized that if he had gone 24 mph faster, he would have arrived 12 hours sooner. How fast did he actually ride?

Need an answer fast

Explanation:

distance = rate*time

90 = r*t

where r is the slower speed and t is the time it takes when going that slower speed.

If r is bumped up 24 mph faster, to r+24, then Santos takes t-12 hours to get there. The second equation is

90 = (r+24)(t-12)

We can solve the first equation for r to get r = 90/t

Then plug this into the second equation and do a bit of algebra

90 = (r+24)(t-12)

90 = (90/t+24)*(t-12)

90 = 90 - 1080/t + 24t - 288

90t = 90t - 1080 + 24t^2 - 288t

0 = 90t - 1080 + 24t^2 - 288t-90t

0 = 24t^2 - 288t - 1080

24t^2 - 288t - 1080 = 0

If you apply the quadratic formula, then you should get the two solutions t = -3 and t = 15. Due to time constraints, I'll skip these steps.

We'll ignore the negative t value. It makes no sense to have a negative time.

So we focus on t = 15 as the only solution.

If t = 15, then,

r = 90/t

r = 90/15

r = 6

Santos rode his bike at 6 mph at first. Going this speed means he takes 15 hours.

If he rode 24 mph faster, at 6+24 = 30 mph, then he would ride for 15-12 = 3 hours instead. Note that 90/30 = 3.

yes

step-by-step explanation:

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,