City Connections: Fractional Unit Rates

Use unit rates to check a bus and subway trip planner.

Travel Rates

Find each requested unit rate. Assume travel rates stay constant within each problem. Write numerical answers as whole numbers or simplified fractions.

The planner records a city bus traveling 3/4 mile in 1/12 hour.

What is the bus's speed? miles per hour

A subway train travels 3 1/2 miles in 1/8 hour. What speed should the planner display?

A. 7/16 mile per hourB. 4/7 mile per hourC. 14 miles per hourD. 28 miles per hour

Imani walks 5/8 mile from a bus stop to a subway entrance in 1/4 hour.

What walking speed should the planner use? miles per hour

An express subway segment takes 3/4 minute to cover 1/2 mile. This planner screen shows time per mile, not miles per minute.

What time per mile should it show? minutes per mile

The planner compares two recorded segments.

Recorded Travel
Service	Distance (miles)	Time (hours)
Bus	5/6	1/18
Subway	2 1/4	1/12

How much greater is the subway's speed than the bus's speed? miles per hour

Rates Behind the Planner

Pay attention to the order of the units. Divide the quantity named first by the quantity named after “per.”

A distance-based shuttle fare is 3/4 dollar for a 3/8-mile ride. Which calculation gives the fare in dollars per mile?

A. (3/4) + (3/8) = 9/8 dollars per mileB. (3/4) × (3/8) = 9/32 dollar per mileC. (3/4) ÷ (3/8) = 2 dollars per mileD. (3/8) ÷ (3/4) = 1/2 dollar per mile

The planner's energy screen shows that an electric bus uses 7/8 kilowatt-hour to travel 1 1/4 miles.

What is its energy use per mile? kilowatt-hour per mile

Before adding walking routes around subway stations, a survey team checks the sidewalks in a 3/8-square-mile area. The check takes 1/4 hour.

At that rate, how much area does the team check per hour? square miles per hour

Another team spends 2/3 hour checking bus-stop locations across a 5/6-square-mile area. The planner tracks this team's time per square mile.

What is the team's time per square mile? hour per square mile

Check the Connections

Use unit rates to compare routes and test estimates. Ignore waiting time unless a problem includes it.

10.

Two shuttle routes connect bus stops with subway entrances. Which statement correctly compares their speeds?

Shuttle Route Records
Route	Distance (miles)	Time (hours)
Cedar	4/5	1/15
Union	7/8	1/16

A. Cedar is faster by 1 mile per hour.B. Union is faster by 2 miles per hour.C. Union is faster by 1 mile per hour.D. Cedar is faster by 2 miles per hour.

11.

Mateo walks 7/12 mile in 1/6 hour between transit stops. The planner uses the same walking speed for a longer transfer. The longer transfer allows 20 minutes, which is 1/3 hour.

What is Mateo's walking speed? miles per hour
How far can he walk in the 20-minute transfer? miles

12.

A bus travels 1 1/4 miles in 1/12 hour. A rider needs to travel 4 miles in 1/4 hour to reach a subway connection. At the same speed, can this bus cover the distance in time?

A. No; the bus travels 15 miles per hour, and the trip requires 16.B. Yes; the bus travels 16 miles per hour, and the trip requires 15.C. No; the bus travels 5 miles per hour, and the trip requires 16.D. Yes; the bus travels 15 miles per hour, and the trip requires 1.

13.

A subway train travels 1 1/8 miles in 3/40 hour. Noor divides (3/40) ÷ (9/8) and labels the result “miles per hour.” Explain what Noor's result actually measures. Then find the correct speed in miles per hour.