A church and a flower shop, 1500 m apart, are situated between Roshel's house and Irene's house. The flower shop is halfway between the two houses and the church is closer to Irene's house. Roshel and Irene left their homes at the same time and arrived at the church at the same time. Roshel drove at a speed of 68 km/h while Irene drove at a speed 16 km/h slower than Roshel. Leaving your answer in kilometres,

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

(a)
Let the distance between Roshel's house and Irene's house be 1 d.
Irene travelled = ¹₂ d - 1500 m
Roshel travelled = ¹₂ d + 1500 m

Distance that Roshel travelled more than Irene
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Roshel took to travel to the church
= 3 ÷ 16
= ³₁₆ h

Distance that Roshel travelled
= ³₁₆ x 68
= 12.75 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Irene's house and the flower shop
= 12.75 - 1.5
= 11.25 km

Answer(s): (a) 3 km; (b) 11.25 km