A church and a flower shop, 1500 m apart, are situated between Jane's house and Vanessa's house. The flower shop is halfway between the two houses and the church is closer to Vanessa's house. Jane and Vanessa left their homes at the same time and arrived at the church at the same time. Jane drove at a speed of 68 km/h while Vanessa drove at a speed 20 km/h slower than Jane. Leaving your answer in kilometres,

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

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

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

(b)
Time that Jane took to travel to the church
= 3 ÷ 20
= ³₂₀ h

Distance that Jane travelled
= ³₂₀ x 68
= 10.2 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Vanessa's house and the flower shop
= 10.2 - 1.5
= 8.7 km

Answer(s): (a) 3 km; (b) 8.7 km