Word problem involving a U.S. Customary length conversion
Two moves in a fixed order: divide to get one lap, then convert to the unit asked for. Doing them the other way round still works, but only if you keep track of what the number means.
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ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.
John cycled 9 laps on a bicycle path around a lake, each the same length. He cycled a total of 39.6 mi.
What was the length of each lap, in feet? Type just the number.
A hiking trail is 2.75 mi long.
How long is it in yards? Use 1760 yd = 1 mi. Type just the number.
A runner completes 5 laps totalling 8,800 yd.
How long is one lap in miles? Use 1760 yd = 1 mi. Type just the number.
Maya cycled 8 laps on a bicycle path around a lake. Each lap was the same length. If she cycled a total of 26.4 mi, what was the length of each lap around the lake?
Write your answer in feet.
| Conversion facts for length | |
|---|---|
| 12 inches (in) | = 1 foot (ft) |
| 3 feet (ft) | = 1 yard (yd) |
| 5280 feet (ft) | = 1 mile (mi) |
| 1760 yards (yd) | = 1 mile (mi) |
Use the table of conversion facts as necessary, and do not round your answer.
Which comes first?
One lap, in miles
Convert to feet
The check that takes two seconds
Eight laps of 17,424 ft is 139,392 ft, and 139,392 ÷ 5280 = 26.4 mi. Back to where you started.
More usefully: a lap of 3.3 miles is a plausible loop around a lake, and 17,424 feet is a plausible number of feet for that. If your answer had come out as 2,178 (dividing by 5280 instead of multiplying) or 139,392 (forgetting to divide), neither would survive a moment's thought.