15 points: after traveling exactly half of its journey from station a to station b, a train was held up for 10 minutes. in order to arrive at city b on schedule, the engine driver had to increase the speed of the train by 12 km/hour. find the original speed of the train before it was held up, if it is known that the distance between the two stations is 120 km.

So let's just mke things easier by imagining that x (km/h) was the original speed of the train.

From the information, we can conclude that:

- The train's speed when it went from station A to the stopping point was x (km/h) => The time it took to finish the first half of its journey was 60/x (h)

- The speed of the train when it went from the stopping point to station B was

x + 12 (km/h) => The time it took to finish the other half of its journey was

60/x + 12 (h)

- The original time the train was supposed to take to finish the whole journey was 120/x (h)

Since the train still arrived at city B on schedule, we have:

   120/x = 60/x + 60/x + 12 + 1/6

⇔ 6 × 120 × (x + 12) = 6 × 60 × (x+12) + 6 × 60x + x(x + 12)

⇔ 720x + 8640 = 360x + 4320 + 360x + x² + 12x

⇔ 720x - 360x - 360x - x² - 12x = -8640 + 4320

⇔ - x² - 12x = -4320

⇔ -x² - 12x + 4320 = 0

⇔ -x² + 60x - 72x + 4320 = 0

⇔ -x(x - 60) - 72(x - 60) = 0

⇔ (-x - 72)(x - 60) = 0

⇔ -x - 72 = 0 or x - 60 = 0

⇔ -x = 72 or x = 60

⇔ x = -72 or x = 60

Since we know that the time can't be a negative number, the only available option left is 60 km/h.

it's d

step-by-step explanation:

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.