A church and a flower shop, 2500 m apart, are situated between Xylia's house and Mary's house. The flower shop is halfway between the two houses and the church is closer to Mary's house. Xylia and Mary left their homes at the same time and arrived at the church at the same time. Xylia drove at a speed of 68 km/h while Mary drove at a speed 16 km/h slower than Xylia. Leaving your answer in kilometres,

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

(a)
Let the distance between Xylia's house and Mary's house be 1 d.
Mary travelled = ¹₂ d - 2500 m
Xylia travelled = ¹₂ d + 2500 m

Distance that Xylia travelled more than Mary
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Xylia took to travel to the church
= 5 ÷ 16
= ⁵₁₆ h

Distance that Xylia travelled
= ⁵₁₆ x 68
= 21.25 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Mary's house and the flower shop
= 21.25 - 2.5
= 18.75 km

Answer(s): (a) 5 km; (b) 18.75 km