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MAT-144 · In-person sections Exam 1 Review · Unit 1
Exam 1 Review · Q14

Converting between compound units: advanced

A rate has a top and a bottom, and here both change. They move in opposite directions, which is the only hard thing about the question and the reason ALEKS labels it advanced.

01 Worked Example Video

Every step of Converting between compound units: advanced explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE
02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

The ALEKS version

A parachutist’s rate during free fall reaches 144 miles per hour.

What is this rate in feet per second? Use 1 mi = 5280 ft. Type just the number.

Metric, same shape

A train travels at 90 kilometres per hour.

What is this in metres per second? Use 1 km = 1000 m. Type just the number.

Running it backwards

A cyclist travels at 30 feet per second.

What is this in miles per hour? Use 1 mi = 5280 ft. Round to two decimal places.

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 The Rule
the numerator converts like any length miles to feet: multiply by 5280
the denominator converts the other way hours to seconds: divide by 3600
Per hour means the hours are already downstairs. Turning them into seconds makes the denominator a bigger number, so the rate gets smaller — a car does far fewer feet per second than it does per hour. Both conversions happen in one chain, and they pull in opposite directions.
Common slips
(1) Converted only the top. 108 × 5280 = 570,240 is feet per hour, not per second. (2) Multiplied by 3600 instead of dividing. That gives a number in the billions, which is wrong in a way you can see. (3) Used the unconverted rate for the distance. The time is in seconds, so the rate must be too.
04 Practice — Step by Step
Top up, bottom down

A skier’s speed during a descent reaches 108 miles per hour.

What is this rate in feet per second? At this rate, how many feet will the skier travel during 7 seconds?

In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answers.

Step 1

What happens to the hours?

Miles per hour becomes feet per second. The hours are on the bottom. To turn them into seconds, do you multiply or divide by 3600?
Step 2

Convert the top

108 miles in feet. Use 1 mi = 5280 ft.
Step 3

Convert the bottom

570,240 feet per hour, in feet per second.
Step 4

Now use the rate

How far in 7 seconds?
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MAT-144 · EXAM 1 REVIEW · Q14 OF 20