Pre Algebra Word Problem

Question

The equation d=rt is used to calculate distance, rate, or time, where d is the distance (in meters), r is the rate (in meters per minute), and t is the time (in minutes). Consider the statements below that describe the walking rates for three people. Graph the equation that represents the rate of the fastest person.

Tomas walks 1200 meters in 8 minutes.

Becky walks for 10 minutes and goes 1400 meters.

Derrick walks at a rate of 145 meters per minute.

Answer 1

We're given the relationship: distance = rate x time (or d=rt), which is crucial to the problem. Particularly, we can solve the equation for r: r = d/t. Now, we're given the rates of three individuals, but notice only one is in meters/min, the other two are only a distance walked and the time taken to walk the distance for each individual. Makes it a little harder to determine who is the faster walker. But using the formula r=d/t, we can find the associated rates in m/min for all individuals, in the same units, which makes for easy comparison.

Tomas: 1200m/8min = 150 m/min

Becky: 1400m/10min = 140m/min

Derrick: 145m/min

From here, it is easy to see who is the faster walker.

For the second part of the question: graphing the equation. We're looking to graph d=rt for each individual with the respective rate of the person put in for r, where t is the independent variable and d is the dependent variable. For example, (Tomas) d = 150t. Notice this is a linear equation with slope 150 and y-intercept 0.