Question

A screenshot is attached (In this level, students use ratios to convert measurement units. Students convert inches to miles and seconds to hours and then use these values to find the unit rate in miles per hour. Students then compare the speed of the remote control car to that of a real car traveling on the highway.)

Answer 1

The remote-control car is going about 2 miles per hour, which is 58 miles per hour slower than a regular car traveling on the freeway.

Conversion Ratios

We can convert seconds to hours using the unit ratio:

`\frac{3,600 \text{ sec}}{1 \text{ hr}}`

We can convert inches to miles using the unit ratio:

`\frac{1 \text{ mi}}{63,360 \text{ in}}`

Solution

We can represent the speed of the remote-control car as:

`\frac{115 \text{ in}}{3.21 \text{ sec}}`

Using the above conversion ratios, we can convert this speed to miles per hour so that it can be compared to a regular car.

`\frac{115 \text{ in}}{3.21 \text{ sec}} * \frac{1 \text{ mi}}{63,360 \text{ in}} * \frac{3,600 \text{ sec}}{1 \text{ hr}}`

`\frac{115 \\ot \text{in}}{3.21 \\ot \text{sec}} * \frac{1 \text{ mi}}{63,360 \\ot \text{in}} * \frac{3,600 \\ot \text{sec}}{1 \text{ hr}}`

↓ canceling units

`(115)/(3.21) * \frac{1 \text{ mi}}{63,360} * \frac{3,600}{1 \text{ hr}}`

↓ simplify multiplication

`\frac{414,000 \text{ mi}}{203,385.6 \text{ hr}}`

↓ separate out units

`(414,000)/(203,385.6) \text{ mph}`

↓ plug into a calculator or approximate using long division

`\boxed{2.03554 \text{ mph}}`

So, the speed of the RC car is approximately 2 miles per hour.

This is about 58 miles per hour slower than a regular car going 60 miles per hour on the freeway.