A church and a flower shop, 2000 m apart, are situated between Mary's house and Risa's house. The flower shop is halfway between the two houses and the church is closer to Risa's house. Mary and Risa left their homes at the same time and arrived at the church at the same time. Mary drove at a speed of 69 km/h while Risa drove at a speed 15 km/h slower than Mary. Leaving your answer in kilometres,

1. how much farther did Mary travel than Risa?
2. how far is Risa's house from the flower shop?

(a)
Let the distance between Mary's house and Risa's house be 1 d.
Risa travelled = ¹₂ d - 2000 m
Mary travelled = ¹₂ d + 2000 m

Distance that Mary travelled more than Risa
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Mary took to travel to the church
= 4 ÷ 15
= ⁴₁₅ h

Distance that Mary travelled
= ⁴₁₅ x 69
= 18.4 km

1000 m = 1 km
2000 m = 2 km

Distance between Risa's house and the flower shop
= 18.4 - 2
= 16.4 km

Answer(s): (a) 4 km; (b) 16.4 km