Distance, Rate, and Coin Problems

The video tutorial covers solving word problems involving nickels and dimes, using substitution to find the number of each coin. It also explores a pattern of squares to determine the number in the 12th diagram and calculates when Dan catches up with Grace, given their biking speeds and start times.

Brit has a total of 40 coins consisting of nickels and dimes, amounting to $2.25. How many nickels does she have?

• 25

• 35

• 40

• 30

In the problem involving nickels and dimes, what is the value of 'd' if 'n' is 35?

• 15

• 10

• 20

• 5

What is the total value of 35 nickels?

• $1.50

• $2.25

• $1.75

• $2.00

In the pattern of squares, how many squares are in the 12th diagram?

• 22

• 21

• 23

• 24

What is the formula used to calculate the number of squares in the nth diagram?

• n + n - 1

• 2n - 1

• n^2 - 1

• n^2 + n

Grace starts biking at 12 mph, and Dan starts an hour later at 15 mph. How long will it take Dan to catch up with Grace?

• 6 hours

• 5 hours

• 4 hours

• 3 hours

If Dan bikes for 4 hours, how far will he have traveled?

• 55 miles

• 45 miles

• 50 miles

• 60 miles

How many hours will Grace have been biking when Dan catches up with her?

• 6 hours

• 5 hours

• 4 hours

• 7 hours

What is the distance at which Grace and Dan meet?

• 60 miles

• 55 miles

• 50 miles

• 65 miles

What is the relationship between distance, rate, and time used in the cyclists' problem?

• Distance = Rate / Time

• Distance = Rate * Time

• Distance = Rate - Time

• Distance = Rate + Time