Grade 7 · Unit 1 · Lesson 8 · part 4 of 5
Emily and the bell
Emily's ride.
Emily and the bell
Emily's ride. Emily leaves for school on her bike at 8:25. By 8:29 and 30 seconds she has gone 34 of a mile. The school is 3.42 miles away and the bell rings at 8:50. Does she make it?
- Find the time so far. From 8:25 to 8:29:30 is 412 minutes.
- Find the unit rate. She knows the miles and wants minutes, so she wants minutes per mile: make the miles 1. What do I multiply 34 mile by to get 1 mile? Its reciprocal, 43. Multiply the minutes by the same number: 412 × 43 = 92 × 43 = 366 = 6 minutes per mile.
- Multiply by the whole distance. 3.42 miles × 6 minutes per mile = 20.52 minutes, about 2012 minutes.
- Answer the question. 8:25 plus 2012 minutes is about 8:45:30. The bell rings at 8:50. Yes, she makes it, with about 412 minutes to spare.
Every piece of the unit is in that one problem: a rate with fractions (Lesson 1), a proportional relationship that always multiplies by the same number (Lessons 2 and 3), the unit rate chosen to answer the question (minutes per mile, because she knows the miles), and the equation t = 6d in action (Lesson 5).
Which way, when? Unit rate way: find how much for one, then multiply. Scale factor way: find how many times bigger, then multiply both. They always agree. Pick the friendlier numbers, and check with the other.