Jason left Town C for Town D at 12.50 p.m. He travelled at an average speed of 60 km/h. At 1.30 p.m., Peter left Town C for Town D, travelling along the same route at an average speed of 90 km/h. At what time did Peter overtake Jason? Ans : ___ p.m.

1. Find the time difference between Jason's and Peter's departure

From $12.50\text{ p.m.}$ to $1.30\text{ p.m.}$ is $40\text{ minutes}$.
$40\text{ minutes} = \frac{40}{60}\text{ h} = \frac{2}{3}\text{ h}$

2. Calculate the distance Jason travelled before Peter started

$\text{Distance} = \text{Speed} \times \text{Time}$
$\text{Distance} = 60 \times \frac{2}{3} = 40\text{ km}$

3. Calculate the relative speed and time taken for Peter to catch up

$\text{Relative speed} = 90 - 60 = 30\text{ km/h}$
$\text{Time taken to catch up} = \frac{40}{30} = \frac{4}{3}\text{ h} = 1\text{ h } 20\text{ min}$

4. Determine the time Peter overtook Jason

$1.30\text{ p.m.} + 1\text{ h } 20\text{ min} = 2.50\text{ p.m.}$