A church and a flower shop, 500 m apart, are situated between Penelope's house and Victoria's house. The flower shop is halfway between the two houses and the church is closer to Victoria's house. Penelope and Victoria left their homes at the same time and arrived at the church at the same time. Penelope drove at a speed of 61 km/h while Victoria drove at a speed 10 km/h slower than Penelope. Leaving your answer in kilometres,

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

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

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

(b)
Time that Penelope took to travel to the church
= 1 ÷ 10
= ¹₁₀ h

Distance that Penelope travelled
= ¹₁₀ x 61
= 6.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Victoria's house and the flower shop
= 6.1 - 0.5
= 5.6 km

Answer(s): (a) 1 km; (b) 5.6 km