A pastry shop and a flower shop, 2500 m apart, are situated between Gillian's house and Pamela's house. The flower shop is halfway between the two houses and the pastry shop is closer to Pamela's house. Gillian and Pamela left their homes at the same time and arrived at the pastry shop at the same time. Gillian drove at a speed of 68 km/h while Pamela drove at a speed 16 km/h slower than Gillian. Leaving your answer in kilometres,

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

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

Distance that Gillian travelled more than Pamela
= 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 ÷ 16
= ⁵₁₆ h

Distance that Gillian travelled
= ⁵₁₆ x 68
= 21.25 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Pamela's house and the flower shop
= 21.25 - 2.5
= 18.75 km

Answer(s): (a) 5 km; (b) 18.75 km