Super-Hard SAT Data Analysis Question 50 | Free SAT Prep

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Question 50·50 Super-Hard SAT Problem Solving and Data Analysis Questions·Problem Solving and Data Analysis

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A drone makes a nonstop research flight consisting of two straight segments. The first segment accounts for 30% of the total flight distance. The drone's speed during the first segment is 25% greater than its speed during the second segment. If the total flight time is 141 minutes, how many minutes does the drone spend on the second segment?

Your answer

When a problem compares distances and speeds, do not assume that the distance ratio is also the time ratio. Write time as distance divided by speed, so a larger speed decreases the corresponding time. Convert percentages to simple ratios first, then combine the distance and speed ratios before using the total time.

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Convert the percentage to a ratio

If the first segment is 30% of the total distance, determine what percentage is the second segment and write the two distances as a ratio.

Convert the speed comparison

A speed that is 25% greater than another speed can be written as $125\%:100\%$ , then simplified.

Use distance divided by speed

For each segment, time is distance divided by speed. Use the distance ratio and speed ratio to create a ratio of the two travel times.

Desmos Guide

Set up the time relationship

Algebra is faster for this question. First determine that the first-segment time is $\frac{12}{35}$ of the second-segment time.

Graph the total-time equation

Let $x$ represent the number of minutes spent on the second segment. Enter $y=\frac{12}{35}x+x$ and $y=141$ .

Read the intersection

Click the intersection of the two graphs. Its $x$ -coordinate gives the time for the second segment.

Step-by-step Explanation

Write the distance and speed ratios

Since the first segment is 30% of the total distance, the second segment is 70% of the total distance. Therefore, the distance ratio is $3:7$ .

A speed that is 25% greater is $125\%$ of the original speed, so the speed ratio for the first segment to the second segment is $5:4$ .

Find the ratio of the travel times

Time is distance divided by speed. Thus, the ratio of the first travel time to the second travel time is

\frac{3}{5}:\frac{7}{4}=12:35

Use the total time

The total number of ratio parts is $12+35=47$ . Since the total time is 141 minutes, each part represents

\frac{141}{47}=3

minutes. The second segment represents 35 parts, so its time is $35\cdot 3=105$ minutes.

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