A runner's pace is measured in minutes per kilometer. Runner A's pace is 25% greater than Runner B's pace. Runner A completes a -kilometer course in minutes at a constant pace. At a constant pace, how many minutes would Runner B take to complete a -kilometer course?
For pace problems, remember that pace is time per unit of distance, so a lower pace means less time for the same distance. Compare the two paces as a fraction, compare the two distances as a fraction, and multiply those factors by the known time. This avoids finding either runner's actual pace.
Hints
Interpret pace carefully
A greater pace means more minutes are needed for each kilometer. Determine the fraction that represents Runner B's pace compared with Runner A's pace.
Compare rather than calculate individual paces
Compare Runner B's distance with Runner A's distance, then combine that distance factor with the pace factor.
Use the time relationship
Since time equals distance times pace, multiply Runner A's time by both comparison factors.
Desmos Guide
Use ratio reasoning first
Algebraic comparison is faster here because the unknown values of and the individual paces cancel.
Verify the combined factor
In the Desmos expression line, enter 15*(15/10)*(4/5). The result verifies the coefficient of after multiplying the distance factor by the pace factor.
Step-by-step Explanation
Relate the paces
If Runner B's pace is minutes per kilometer, then Runner A's pace is . Therefore, Runner B's pace is of Runner A's pace.
Compare the distances
Runner B runs kilometers, while Runner A runs kilometers. Thus, Runner B's distance is times Runner A's distance.
Find Runner B's time
Time equals distance times pace. Relative to Runner A's time, Runner B's time is multiplied by for the longer distance and by for the lower pace.