Question

Phil is riding his bike. He rides 25 miles in 2 hours, 37.5 miles in 3 hours, and 50 miles in 4 hours. Write an equation to describe the situation (Hint: Find the constant of proportionality in order to help you write the equation).

a) y=12.5x
b) y=15x
c) y=10x
d)y=20x

Answer 1

Phil's constant biking speed is 12.5 mph, which gives us the equation y = 12.5x, where y is the distance and x is the time in hours. This corresponds to option (a).

Step-by-step explanation:

The student has provided various distances traveled by Phil on his bike and the corresponding time it took to cover those distances. To write an equation that describes this situation, we need to determine the constant of proportionality, which is the same as finding the speed in this context.

For all given data points, we divide the distance by the time:

1. 25 miles ÷ 2 hours = 12.5 mph
2. 37.5 miles ÷ 3 hours = 12.5 mph
3. 50 miles ÷ 4 hours = 12.5 mph

Since the speed is constant at 12.5 mph, we can use this to write the equation in the form y = mx, where y represents the distance traveled, m is the constant speed, and x is the time in hours. The equation that describes this situation is thus:

y = 12.5x

The correct answer aligns with option (a).