A church and a flower shop, 500 m apart, are situated between Penelope's house and Zoe's house. The flower shop is halfway between the two houses and the church is closer to Zoe's house. Penelope and Zoe left their homes at the same time and arrived at the church at the same time. Penelope drove at a speed of 77 km/h while Zoe drove at a speed 14 km/h slower than Penelope. Leaving your answer in kilometres,

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

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

Distance that Penelope travelled more than Zoe
= 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 ÷ 14
= ¹₁₄ h

Distance that Penelope travelled
= ¹₁₄ x 77
= 5.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Zoe's house and the flower shop
= 5.5 - 0.5
= 5 km

Answer(s): (a) 1 km; (b) 5 km