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John left Town M at 0600 and travelled towards Town
N at a constant speed of
54km//h. Ben left Town M, 20 minutes after John and travelled towards Town N at a constant speed of
63km//h. At what time after Ben started will he overtake John on the way?

$2$ . John left Town M at $0600$ and travelled towards Town $N$ at a constant speed of $54 \mathrm{~km} / \mathrm{h}$ . Ben left Town M, $20$ minutes after John and travelled towards Town N at a constant speed of $63 \mathrm{~km} / \mathrm{h}$ . At what time after Ben started will he overtake John on the way?

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Pythagorean theorem

Full solution

Q.

2

. John left Town M at

0600

and travelled towards Town

N

at a constant speed of

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

. Ben left Town M,

20

minutes after John and travelled towards Town N at a constant speed of

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

. At what time after Ben started will he overtake John on the way?

Calculate Time Difference: Calculate the time difference between John's and Ben's start times. John starts at $0600$ , and Ben starts $20$ minutes later at $0620$ .
Determine John's Distance: Determine the distance John travels before Ben starts. $\newline$ John's speed = $54\,\text{km/h}$ . $\newline$ Time = $20$ minutes = $\frac{20}{60}$ hours = $\frac{1}{3}$ hours. $\newline$ Distance = Speed $\times$ Time = $54\,\text{km/h} \times \frac{1}{3}\,h = 18\,km$ .
Set Up Catch-Up Equation: Set up the equation to find the time when Ben catches up to John. $\newline$ Let $t$ be the time in hours after Ben starts at $0620$ . $\newline$ Distance John travels = $18$ km + $54t$ km. $\newline$ Distance Ben travels = $63t$ km. $\newline$ Set distances equal to find $t$ when Ben catches up: $63t = 18 + 54t$ .
Solve for t: Solve the equation for t. $\newline$ $63t = 18 + 54t$ . $\newline$ $63t - 54t = 18$ . $\newline$ $9t = 18$ . $\newline$ $t = \frac{18}{9}$ . $\newline$ $t = 2$ hours.
Calculate Actual Time: Calculate the actual time of day when Ben overtakes John. Ben starts at $0620$ , plus $2$ hours = $0820$ .

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