Question

If Laura were able to increase her average cycling speed by 3.5 km/h, she would be able to cover in 2 hours a distance at least as great as that which now takes 3 hours. What is her best average speed at present?

Answer 1

Laura's current average speed is 7 km/h. We solve this by setting up an equation based on the information provided and finding the speed at which she currently covers a certain distance in 3 hours that she could cover in 2 hours if she sped up by 3.5 km/h.

Step-by-step explanation:

If Laura were to increase her average cycling speed by 3.5 km/h, she could cover the same distance in 2 hours that currently takes her 3 hours. To find Laura's current average speed, we can use the formula for average speed, Vavg = distance / time.

Let's assume the distance Laura currently covers in 3 hours is D kilometers. Hence, her current average speed is Vavg = D / 3 km/h.

If she increases her speed by 3.5 km/h, her new average speed would be (D / 3) + 3.5 km/h, and she'd cover the distance D in 2 hours at this speed.

So, (D / 3) + 3.5 = D / 2. Solving this equation for D, we would find that Laura's current average speed is the variable we solve for in this equation.

Multiplying both sides of the equation by 6 to clear the denominators:
2D + 21 = 3D

Subtracting 2D from both sides:
21 = D

Now, substituting back into the original average speed formula:
Vavg = 21 km / 3 h = 7 km/h

Therefore, Laura's best average speed at present is 7 km/h.