The cue is pace in minutes per kilometer: multiply it by distance to get time. Find A's pace, use the percent comparison to find B's, then apply B's pace to B's course. Desmos can handle the final numerical calculation. Watch the direction: a greater pace means more minutes per kilometer, not a faster runner.
Hints
- Hint 1
A pace is minutes per kilometer, not kilometers per minute. Divide A's time by A's course length to get the rate you'll compare with B's.
- Hint 2
A percent comparison needs a base, the amount the percent is measured against. Here, B's pace is the base, so A's pace is times B's. How would you undo that multiplier?
- Hint 3
At a constant pace, every kilometer takes the same number of minutes. Multiply B's pace in minutes per kilometer by B's course length in kilometers to find B's time.
Step-by-step
Find B's pace, then B's time
Step 1Find A's pace
A pace measures minutes per kilometer, so divide A's minutes by A's kilometers:
Here means A's pace in minutes per kilometer.
- Step 2
Write the percent comparison
The base, the pace the is measured against, is B's pace. Call that pace . A's pace is , or times, B's pace:
A greater pace means more minutes per kilometer, not more kilometers per minute.
- Step 3
Solve for B's pace
To get B's pace, divide both sides by :
Multiplying A's pace by instead would reverse which runner has the greater pace.
- Step 4
Turn B's pace into a time
B runs kilometers. Distance times pace gives time because kilometers cancel with the kilometers in minutes per kilometer:
Here means B's time in minutes.
- Step 5
Replace B's pace
Substitute into the time equation:
- Step 6
Replace A's pace
Use the pace found from A's time and distance in place of :
- Step 7
Cancel the course-distance letter
The course lengths are positive, so isn't zero. Cancel from the top and bottom, leaving with the time:
- Step 8
Calculate B's time
Type into Desmos. It returns , so B takes minutes to complete the -kilometer course. Choice D.