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Julianna started from Point
A and drove towards Point
B at a constant speed of
60km//h. Half an hour later, Tom started from Point A and drove along the same route at a constant speed of
80km//h. How long after Tom started will he overtake Julianna on the way?

$1$ . Julianna started from Point $A$ and drove towards Point $B$ at a constant speed of $60 \mathrm{~km} / \mathrm{h}$ . Half an hour later, Tom started from Point A and drove along the same route at a constant speed of $80 \mathrm{~km} / \mathrm{h}$ . How long after Tom started will he overtake Julianna on the way?

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Pythagorean theorem

Full solution

Q.

1

. Julianna started from Point

A

and drove towards Point

B

at a constant speed of

60 \mathrm{~km} / \mathrm{h}

. Half an hour later, Tom started from Point A and drove along the same route at a constant speed of

80 \mathrm{~km} / \mathrm{h}

. How long after Tom started will he overtake Julianna on the way?

Calculate Distance Before Tom Starts: Calculate the distance Julianna travels before Tom starts. $\newline$ Julianna's speed = $60 \, \text{km/h}$ , Time = $0.5 \, \text{hours}$ . $\newline$ Distance = Speed $\times$ Time = $60 \, \text{km/h} \times 0.5 \, \text{h} = 30 \, \text{km}$ .
Set Up Equation to Find Time: Set up the equation to find the time $t$ it takes for Tom to catch up to Julianna. $\newline$ Tom's speed = $80$ km/h, Julianna's speed = $60$ km/h. $\newline$ Relative speed = Tom's speed - Julianna's speed = $80$ km/h - $60$ km/h = $20$ km/h. $\newline$ Tom needs to cover the initial $30$ km gap. $\newline$ Time = Distance / Relative speed = $30$ km / $20$ km/h = $1.5$ hours.

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