Two couriers leave delivery hubs R and S, which are 211 km apart, travelling toward one another. The courier from R travels at 48 km/h and begins 30 minutes before the courier from S, who travels at 52 km/h. After how many hours from the departure of the courier at R will they meet?

The correct answer is 2.37 h.

Step 1: Calculate the distance covered by the courier from R before the courier from S departs.
The courier from hub R starts 30 minutes (which is 0.5 hours) earlier than the courier from hub S, traveling at a speed of 48 km/h.
$\text{Distance traveled by courier R initially}=\text{Speed}\times \text{Time}$
$\text{Distance traveled by courier R initially}=48\text{km/h}\times 0.5\text{h}=24\text{km}$
Thus, courier R covers 24 km before courier S begins moving.

Step 2: Calculate the remaining distance between the two couriers.
Subtract the 24 km already covered by courier R from the total initial distance of 211 km:
$\text{Remaining distance}=211\text{km}-24\text{km}=187\text{km}$
When courier S starts, the distance separating the two couriers is 187 km.

Step 3: Determine the relative speed of the two couriers.
Since the two couriers are traveling toward each other, their speeds add together to give their combined relative speed:
$\text{Relative speed}=48\text{km/h}+52\text{km/h}=100\text{km/h}$

Step 4: Find the time taken for them to meet after courier S departs.
Divide the remaining distance by their relative speed:
$\text{Time after S departs}=\frac{\text{Remaining distance}}{\text{Relative speed}}$
$\text{Time after S departs}=\frac{187\text{km}}{100\text{km/h}}=1.87\text{hours}$

Step 5: Calculate the total time elapsed from the departure of the courier at R.
Add the initial 0.5 hours that courier R traveled alone to the 1.87 hours both couriers traveled together:
$\text{Total time}=0.5\text{hours}+1.87\text{hours}=2.37\text{hours}$
They will meet 2.37 hours after the courier at hub R departs.