Two questions: 1.) How many three digit numbers can be formed using only even digits, if the numbers can contain each of these digits only once?

2.) A 400m train is traveling 12km/h. If the train enters a tunnel that is 800m long, how Many minutes will it take for the train to clear the tunnel?

Problem 1

Work Shown:

The set of single digits that are even numbers is {0,2,4,6,8}. There are 5 items here.

The first selection cannot be 0 since a number like 048 is not a three digit number (instead 048 becomes 48 which is a two digit number)

So we have {2,4,6,8} to pick from. There are 4 choices here.

Once we pick a value from that list, we have 5-1 = 4 items left to pick from. For instance, let's say we picked 2 as the first digit. So {0,2,4,6,8} would become {0,4,6,8}

After we pick the second digit, we then have 4-1 = 3 digits to pick from

Overall, there are 4*4*3 = 48 different three digit numbers that can be formed using only even digits, and we cannot repeat a digit.

Problem 2

Work Shown:

400 m = 400/1000 = 0.4 km

800 m = 800/1000 = 0.8 km

The train is 0.4 km long. The tunnel is 0.8 km long.

In order the the train's caboose to clear the tunnel (the very back side of the caboose not be in/under the tunnel), the front of the train's engine must travel 0.8+0.4 = 1.2 km. Any shorter and the train will still be in the tunnel somehow. I recommend drawing out a diagram to see why this is the case.

Since it needs to travel 1.2 km, and its speed is 12 km/hr, this means...

distance = rate*time

d = r*t

1.2 = 12*t

12t = 1.2

t = 1.2/12

t = 0.1

This is the amount of time it takes, in hours, to travel 1.2 km

Multiply by 60 to convert form hours to minutes

0.1 hrs = (0.1 hrs)*(60 min/1 hr) = (0.1*60) min = 6 minutes

0.1 hrs = 6 minutes

The train will take 6 minutes to clear the tunnel.

16 kids because 2 times 8 equals 16