A church and a flower shop, 1000 m apart, are situated between Jean's house and Xandra's house. The flower shop is halfway between the two houses and the church is closer to Xandra's house. Jean and Xandra left their homes at the same time and arrived at the church at the same time. Jean drove at a speed of 78 km/h while Xandra drove at a speed 15 km/h slower than Jean. Leaving your answer in kilometres,

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

(a)
Let the distance between Jean's house and Xandra's house be 1 d.
Xandra travelled = ¹₂ d - 1000 m
Jean travelled = ¹₂ d + 1000 m

Distance that Jean travelled more than Xandra
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Jean took to travel to the church
= 2 ÷ 15
= ²₁₅ h

Distance that Jean travelled
= ²₁₅ x 78
= 10.4 km

1000 m = 1 km
1000 m = 1 km

Distance between Xandra's house and the flower shop
= 10.4 - 1
= 9.4 km

Answer(s): (a) 2 km; (b) 9.4 km