A pastry shop and a flower shop, 2500 m apart, are situated between Eva's house and Cathy's house. The flower shop is halfway between the two houses and the pastry shop is closer to Cathy's house. Eva and Cathy left their homes at the same time and arrived at the pastry shop at the same time. Eva drove at a speed of 76 km/h while Cathy drove at a speed 19 km/h slower than Eva. Leaving your answer in kilometres,

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

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

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

(b)
Time that Eva took to travel to the pastry shop
= 5 ÷ 19
= ⁵₁₉ h

Distance that Eva travelled
= ⁵₁₉ x 76
= 20 km

1000 m = 1 km
2500 m = 2.5 km

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

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