Let's solve each part of the
Rate-Time-Distance Problems step by step.
---
1. Bill runs at a rate of $ r $ mi/h. Will runs twice as fast. Will’s rate is ________ mi/h.
- Bill's rate = $ r $ miles per hour.
- Will runs
twice as fast, so his rate is:
$$
2r \text{ mi/h}
$$
✔ Answer: $ 2r $
---
2. Joshua rides his bike to school in $ k $ min. His sister Rachel takes 15 min longer to walk. She spends ________ min walking to school.
- Joshua's time = $ k $ minutes.
- Rachel takes
15 minutes longer, so her time is:
$$
k + 15 \text{ minutes}
$$
✔ Answer: $ k + 15 $
---
3. Sue and Carol start bicycling toward each other at the same time from homes 9 miles apart. When they meet, Carol has traveled $ c $ mi. Sue has traveled ________ mi.
- Total distance between them = 9 miles.
- They are moving
toward each other, so when they meet, the sum of the distances they've traveled is 9 miles.
- Carol traveled $ c $ miles.
- Therefore, Sue traveled:
$$
9 - c \text{ miles}
$$
✔ Answer: $ 9 - c $
---
✔ Final Answers:
1. Will’s rate is
$ 2r $ mi/h.
2. Rachel spends
$ k + 15 $ min walking to school.
3. Sue has traveled
$ 9 - c $ mi.
These expressions use the given variables and reflect the relationships described in each problem.
Parent Tip: Review the logic above to help your child master the concept of distance rate and time word problems worksheet.
