**Middle School Number Sense Lesson 71: Converting Speed**

We are now getting into the last 10 questions on a number sense test. Today's lesson is an oldie but a goodie--I still remember it from when I competed 25+ years ago... It appeared

**5 times**last year, with a median placement at

**question # 75**.

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The main type of question in this category is converting either direction between

**mph**(miles per hour) and

**fps**(feet per second). Before I tell you the secret ratio here, let's look at it mathematically:

**1 mile 1 hour 1 min 5280 feet**

---------- x ---------- x ---------- x --------------

1 hour 60 min 60 sec 1 mile

---------- x ---------- x ---------- x --------------

1 hour 60 min 60 sec 1 mile

**hour**,

**min**, and

**mile** will cancel out. Once we multiply all the numbers, we are left with

**5280/3600 feet/second**. 5280/3600 reduces to 528/360, which reduces to 264/180, which reduces to 132/90, which reduces to 66/45, which reduces to

**22/15**. So:

**1 mph = 22/15 fps**. Or better yet:

**15 mph = 22 fps**

**Example 1: 30 miles/hour = ___ feet/second**

- Divide by 15. 30 ÷ 15 =
**2** - Multiply by 22. 2 x 22 =
**44**

**Example 2: 88 feet/second = ___ miles/hour**

- Divide by 22. 88 ÷ 22 =
**4** - Multiply by 15. 4 x 15 =
**60**

**Example 3: 7.5 miles/hour = ___ feet/second**

- Divide by 15. 7.5 ÷ 15 =
**.5** - Multiply by 22. .5 x 22 =
**11**

**Example 4: Estimate: * 900 mph = ___ feet/second**

- Divide by 15. 900 ÷ 15 =
**60**. - Multiply by 22. 60 x 22 =
**1320**. We didn't need to estimate on this one.

**Example 5: How long would it take to travel 450 miles at 75 miles per hour? ___ hours**

- Simply divide 450 by 75.
- 450 ÷ 75 = 90 ÷ 15 =
**6**.

**Example 6: What constant speed must you drive in 6 hours to go 342 miles? ___ mph**

- Divide 342 by 6.
- 342 ÷ 6 = 114 ÷ 2 =
**57**.

**Check back soon for a free worksheet to help you practice ConvSpeed.**

**Up Next for Middle School: FunctionExpo**