Ratios and proportions; distance-rate-time — ISEE Upper practice questions

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Practice 105 Ratios and proportions; distance-rate-time questions in the app

What this topic is

Ratios and proportions; distance-rate-time on the ISEE Upper Mathematics Achievement section covers equivalent ratios, similar figures, unit rates, and the relationship among distance, rate, and time.

A student must set up a proportion, scale corresponding sides, convert a linear scale into an area scale, and find an unknown price or production total from a given rate. Items are typically short word problems with four answer choices. Common traps include applying a side-length scale to area without squaring it, swapping the two quantities in a cost ratio, and treating a same-time machine problem as inverse rather than direct variation.

Distance-rate-time questions often hide a unit mismatch or an incorrect average speed.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

A triangle has side lengths 6, 8, and 10 and area 24 square units. A second triangle is similar to it, and the side corresponding to the side of length 8 has length 12. What is the area of the second triangle?

36✗ Not this one48✗ Not this one54✓ Correct81✗ Not this one

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Answer: C — 54

The side-length scale factor is $\dfrac{12}{8}=\dfrac{3}{2}$ . Areas scale by the square of the side-length scale factor, so the area scale factor is $\dfrac{9}{4}$ . The second triangle’s area is $24\times\dfrac{9}{4}=54$ .

Question 2Easier

At a farmers market, seven sacks of rice cost the same as twenty-one sacks of flour. If one sack of flour costs $3, what is the price of one sack of rice?

$3✗ Not this one$9✓ Correct$12✗ Not this one$15✗ Not this one

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Answer: B — $9

Twenty-one sacks of flour cost $21 \times \$3 = \$63$ , and that equals the cost of the 7 sacks of rice, so one sack of rice costs $\$63 \div 7 = \$9$ . (A) just copies the given flour price, while (C) and (D) apply the wrong sack ratio (treating it as $4{:}1$ or $5{:}1$ instead of $3{:}1$ ).

Question 3Easier

5 identical machines produce 150 parts in 6 hours. At the same per-machine rate, how many parts will 7 machines produce in 6 hours?

35✗ Not this one152✗ Not this one210✓ Correct1050✗ Not this one

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Answer: C — 210

Each machine produces $150\div(5\cdot6)=5$ parts per hour. Thus 7 machines produce $7(6)(5)=210$ parts.

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Practice 105 Ratios and proportions; distance-rate-time questions in the app

Ratios and proportions; distance-rate-time — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Mathematics Achievement