A salon and a cafe, 2500 m apart, are situated between Lucy's house and Fanny's house. The cafe is halfway between the two houses and the salon is closer to Fanny's house. Lucy and Fanny left their homes at the same time and arrived at the salon at the same time. Lucy drove at a speed of 72 km/h while Fanny drove at a speed 16 km/h slower than Lucy. Leaving your answer in kilometres,

1. how much farther did Lucy travel than Fanny?
2. how far is Fanny's house from the cafe?

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

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

(b)
Time that Lucy took to travel to the salon
= 5 ÷ 16
= ⁵₁₆ h

Distance that Lucy travelled
= ⁵₁₆ x 72
= 22.5 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Fanny's house and the cafe
= 22.5 - 2.5
= 20 km

Answer(s): (a) 5 km; (b) 20 km