Understanding Distance, Rate, and Time

The video tutorial explains how to solve a word problem involving the biking speeds of Manny and Veronica. Manny rides 3 miles per hour faster than Veronica. The problem is solved using the formula Distance = Rate x Time. By setting up equations for both Manny and Veronica, the tutorial demonstrates how to solve for their respective speeds using algebraic methods, including cross-multiplication. The solution is verified by checking the calculated speeds against the problem's conditions.

What is the relationship between Manny's and Veronica's biking speeds?

• Manny rides 5 miles per hour faster than Veronica.

• Manny rides 3 miles per hour faster than Veronica.

• Veronica rides 3 miles per hour faster than Manny.

• They both ride at the same speed.

If Veronica's speed is represented as R, how can Manny's speed be expressed?

• R / 3

• R + 3

• R - 3

• 3R

What is the equation for Manny's distance traveled?

• 36 = R x T

• 45 = (R + 3) x T

• 45 = R x T

• 36 = (R + 3) x T

How do we express the time taken by both Manny and Veronica?

• T = 36 / R and T = 45 / (R + 3)

• T = 45 / (R + 3) and T = 36 / R

• T = 36 / (R + 3) and T = 45 / R

• T = 45 / R and T = 36 / (R + 3)

What is the next step after equating the two expressions for time?

• Divide the two equations.

• Subtract the two equations.

• Add the two equations.

• Cross-multiply the two equations.

What is the value of R, representing Veronica's speed?

• 18 miles per hour

• 10 miles per hour

• 15 miles per hour

• 12 miles per hour

How fast is Manny riding his bike?

• 10 miles per hour

• 12 miles per hour

• 18 miles per hour

• 15 miles per hour

What is the formula used to solve this problem?

• Time = Distance / Speed

• Speed = Distance / Time

• Distance = Rate x Time

• Distance = Speed x Time

Why is it important to verify the solution in word problems?

• To make the problem more complex.

• To find alternative solutions.

• To practice more equations.

• To ensure the solution is correct and answers the question asked.

What should you do if the times for both individuals are equal?

• Equate their time expressions.

• Add their speeds.

• Multiply their speeds.

• Subtract their speeds.