Converting between compound units

Two-part: convert a compound unit (mph → km/h), then use it to compute a distance over time.

01 Mini-Lesson Video

▸ VIDEO COMING SOON

A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here's an example of what you'll see.

Cyclist speed and distance v1

A cyclist rides her bike at a speed of 10 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 4 hours?

Use 1 mile = 1.6 kilometers. Don't round.

Speed: km/h

Distance in 4 hours: km

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 How to Solve It

speed = rate (units/time)
distance = speed × time

Compound units like mph have a top and a bottom. Convert each piece you need to convert. For this question, just the top (miles → km).

Convert the speed: 10 mph → ? km/h.

The unit on top (mi) needs to become km. The unit on the bottom (h) stays the same, so we only need one factor.

10 mi /h \times 1.6 km 1 mi = 16 km/h

10 × 1.6 = 16. mi cancels; km survives. Hours stay where they were.

Distance in 4 hours.

Distance = speed × time. Use the converted speed (16 km/h), not the original (10 mph), so the answer comes out in km.

16 km/ h \times 4 h = 64 km

Hours cancel between speed and time; km survives.

▸ COMMON SLIPS(1) Don't round. ALEKS asks for the exact answer (10 × 1.6 = 16, exactly). If you round 1.6 to 2 "to make it easier," you'll be off by 4 km. (2) Used the wrong speed. For the distance question, use the CONVERTED speed (16 km/h) so the answer is in km. Using 10 mph × 4 h gives 40 mi, which is the right idea but the wrong unit.

04 Practice — Step by Step

A truck moves at 50 mph. Walk the same two-part question: convert the speed, then compute distances. Use 1 mi = 1.6 km.

Convert the speed: 50 mph → km/h.

Convert 50 miles per hour to kilometers per hour. Use 1 mi = 1.6 km.

speed =

Distance in 2 hours.

Using the converted speed (80 km/h), how far does the truck travel in 2 hours?

distance =

Convert back: 80 km/h → mph.

Now go the other direction. Convert 80 km/h back to mph. Use 1 mi = 1.6 km.

speed =

▸ NICE WORK

You walked compound-unit conversions both ways.

Compound units like mph or km/h have a top and a bottom. Convert each piece that needs converting. For ALEKS Q5, only the top (mi → km) needed to change. Apply the converted speed to the time to get the distance, and remember: don't round when ALEKS says "don't round."

Q4 Q6