A pastry shop and a flower shop, 2000 m apart, are situated between Jade's house and Emma's house. The flower shop is halfway between the two houses and the pastry shop is closer to Emma's house. Jade and Emma left their homes at the same time and arrived at the pastry shop at the same time. Jade drove at a speed of 76 km/h while Emma drove at a speed 19 km/h slower than Jade. Leaving your answer in kilometres,

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

(a)
Let the distance between Jade's house and Emma's house be 1 d.
Emma travelled = ¹₂ d - 2000 m
Jade travelled = ¹₂ d + 2000 m

Distance that Jade travelled more than Emma
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Jade took to travel to the pastry shop
= 4 ÷ 19
= ⁴₁₉ h

Distance that Jade travelled
= ⁴₁₉ x 76
= 16 km

1000 m = 1 km
2000 m = 2 km

Distance between Emma's house and the flower shop
= 16 - 2
= 14 km

Answer(s): (a) 4 km; (b) 14 km