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Chiamaka is $x$ from the university and drives $y$ closer every hour. Valente is $z$ from the university and drives $w$ closer every hour. Let $t$ represent the time, in hours, since Chiamaka and Valente started driving toward the university. Complete the inequality to represent the times when Valente is closer than Chiamaka to the university.

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One-step inequalities: word problems

Full solution

Q. Chiamaka is

x

from the university and drives

y

closer every hour. Valente is

z

from the university and drives

w

closer every hour. Let

t

represent the time, in hours, since Chiamaka and Valente started driving toward the university. Complete the inequality to represent the times when Valente is closer than Chiamaka to the university.

Define Distances: Let's define the distances: Chiamaka starts $100 \, \text{km}$ from the university and drives at $40 \, \text{km/h}$ towards it. Valente starts $150 \, \text{km}$ away and drives at $60 \, \text{km/h}$ towards it. Let $t$ represent the time in hours since they started driving.
Write Expressions: Write the expressions for the distances each has left to travel to the university after $t$ hours. For Chiamaka: Distance = $100 - 40t$ . For Valente: Distance = $150 - 60t$ .
Set Up Inequality: Set up the inequality to find when Valente is closer: 150 - 60t < 100 - 40t.
Simplify Inequality: Simplify the inequality: 150 - 60t < 100 - 40t becomes -60t + 40t < 100 - 150.
Continue Simplifying: Continue simplifying: -20t < -50.
Divide and Reverse: Divide both sides by $-20$ and reverse the inequality sign (since dividing by a negative number): t > 2.5.

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