Unit mismatch sprint

Combine or report quantities in inconsistent units without converting.

An error-pattern drill: practice spotting and avoiding this specific SHSAT trap.

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How to avoid unit-mismatch mistakes

A bus goes 45 miles in 90 minutes. What is its speed in miles per hour? If you divide \(45 \div 90\), you get 0.5, a silly speed. First change 90 minutes to 1.5 hours. Then \(45 \div 1.5 = 30\) miles per hour.

This trap works because the numbers look ready to use. The question gives minutes but asks for hours. Or it gives two ratios that use different sizes for the shared part.

Check habits:

Worked examples

Example 1.
A delivery truck drives 27 miles in 1.5 hours, then 133 miles in 150 minutes. What is the delivery truck's average speed for the entire trip, in miles per hour?
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Answer:
C

Average speed \(=\) total distance \(\div\) total time, NOT the average of the leg speeds. Total distance \(= 27 + 133 = 160\) mi. Total time \(= 1.5 + 150 \div 60 = 4\) h. Average speed \(= 160 \div 4 = 40\) mph. (Averaging the two leg speeds gives 35.6 mph. Writing 150 minutes as 1.5 hours (\(160 \div (1.5 + 1.5)\)) gives about 53.3 mph. Using the first leg's speed only (\(27 \div 1.5\)) gives 18 mph.)

Example 2.
A trip starts at 9:50 p.m. and lasts 310 minutes. At what time does it end?
Show answer and explanation
Answer:
B

\(310\) minutes \(= 5\) h \(10\) min (divide by \(60\), not \(100\)). Add that to 9:50 p.m. to get 3:00 a.m. Passing noon switches a.m. to p.m.; passing midnight switches p.m. to a.m. (Reading 310 minutes as 3 h 10 min (as if an hour had 100 minutes) gives 1:00 a.m. Not switching a.m. and p.m. when passing noon or midnight gives 3:00 p.m. Not carrying the extra 60 minutes into the hour (\(50 + 10 = 60\) minutes) gives 2:00 a.m.)

Example 3.
In a group of students, the ratio of first graders to second graders is 6:5, and the ratio of second graders to third graders is 4:3. What is the combined ratio of first graders to second graders to third graders, in simplest form?
Show answer and explanation
Answer:
D

The shared term is second graders: scale 6:5 by 4 and 4:3 by 5 so both give second graders \(= 20\) (the LCM of 5 and 4). This gives 24:20:15, which is already in lowest terms. (Joining the original numbers without matching second graders gives 6:5:3 or 6:4:3. Writing 20 for second graders but swapping the factors on the outer terms (\(6 \times 5\) and \(3 \times 4\)) gives 30:20:12, which reduces to 15:10:6.)