A salon and a cafe, 1500 m apart, are situated between Xylia's house and Lynn's house. The cafe is halfway between the two houses and the salon is closer to Lynn's house. Xylia and Lynn left their homes at the same time and arrived at the salon at the same time. Xylia drove at a speed of 70 km/h while Lynn drove at a speed 14 km/h slower than Xylia. Leaving your answer in kilometres,

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

(a)
Let the distance between Xylia's house and Lynn's house be 1 d.
Lynn travelled = ¹₂ d - 1500 m
Xylia travelled = ¹₂ d + 1500 m

Distance that Xylia travelled more than Lynn
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Xylia took to travel to the salon
= 3 ÷ 14
= ³₁₄ h

Distance that Xylia travelled
= ³₁₄ x 70
= 15 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Lynn's house and the cafe
= 15 - 1.5
= 13.5 km

Answer(s): (a) 3 km; (b) 13.5 km