A pastry shop and a flower shop, 2500 m apart, are situated between Gillian's house and Zara's house. The flower shop is halfway between the two houses and the pastry shop is closer to Zara's house. Gillian and Zara left their homes at the same time and arrived at the pastry shop at the same time. Gillian drove at a speed of 72 km/h while Zara drove at a speed 18 km/h slower than Gillian. Leaving your answer in kilometres,

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

(a)
Let the distance between Gillian's house and Zara's house be 1 d.
Zara travelled = ¹₂ d - 2500 m
Gillian travelled = ¹₂ d + 2500 m

Distance that Gillian travelled more than Zara
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Gillian took to travel to the pastry shop
= 5 ÷ 18
= ⁵₁₈ h

Distance that Gillian travelled
= ⁵₁₈ x 72
= 20 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Zara's house and the flower shop
= 20 - 2.5
= 17.5 km

Answer(s): (a) 5 km; (b) 17.5 km