A church and a flower shop, 500 m apart, are situated between Tina's house and Fiona's house. The flower shop is halfway between the two houses and the church is closer to Fiona's house. Tina and Fiona left their homes at the same time and arrived at the church at the same time. Tina drove at a speed of 69 km/h while Fiona drove at a speed 12 km/h slower than Tina. Leaving your answer in kilometres,

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

(a)
Let the distance between Tina's house and Fiona's house be 1 d.
Fiona travelled = ¹₂ d - 500 m
Tina travelled = ¹₂ d + 500 m

Distance that Tina travelled more than Fiona
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Tina took to travel to the church
= 1 ÷ 12
= ¹₁₂ h

Distance that Tina travelled
= ¹₁₂ x 69
= 5.75 km

1000 m = 1 km
500 m = 0.5 km

Distance between Fiona's house and the flower shop
= 5.75 - 0.5
= 5.25 km

Answer(s): (a) 1 km; (b) 5.25 km