一个市场和一个体育场相距 240 米。它们位于保罗和拉妮家之间，如下图所示。市场正好位于两座房子的正中间。 一天早上，保罗和拉妮同时从各自的家里骑车出发，并同时到达体育场。拉妮的骑行速度是 100 米/分，而保罗的骑行速度比拉妮快 15 米/分。

1. Express the distances cycled by Paul and Rani in terms of the distance from their houses to the market.

Let the distance from the market to either house be $x$ m (since the market is exactly half-way between the two houses).
Paul's distance to the stadium = $x + 240$ m
Rani's distance to the stadium = $x - 240$ m

2. Calculate the difference in the distances cycled.

Difference = $(x + 240) - (x - 240)$
$= x + 240 - x + 240$
$= 480$ m

1. Find the difference in distance cycled by Paul and Rani (from part a)

Since the market is exactly halfway between their houses, Paul's distance to the market equals Rani's distance to the market. The stadium is $240$ m from the market towards Rani's house.
Difference in distance $= 240 + 240 = 480$ m

2. Calculate the time taken to arrive at the stadium

Difference in speed $= 15$ m/min
Time taken $= \frac{480}{15} = 32$ min

3. Calculate the distance from Rani's house to the stadium

Distance Rani cycled $= 100 \times 32 = 3200$ m