A church and a flower shop, 500 m apart, are situated between Pamela's house and Opal's house. The flower shop is halfway between the two houses and the church is closer to Opal's house. Pamela and Opal left their homes at the same time and arrived at the church at the same time. Pamela drove at a speed of 80 km/h while Opal drove at a speed 10 km/h slower than Pamela. Leaving your answer in kilometres,

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

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

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

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

Distance that Pamela travelled
= ¹₁₀ x 80
= 8 km

1000 m = 1 km
500 m = 0.5 km

Distance between Opal's house and the flower shop
= 8 - 0.5
= 7.5 km

Answer(s): (a) 1 km; (b) 7.5 km