A salon and a cafe, 1500 m apart, are situated between Zoe's house and Wendy's house. The cafe is halfway between the two houses and the salon is closer to Wendy's house. Zoe and Wendy left their homes at the same time and arrived at the salon at the same time. Zoe drove at a speed of 68 km/h while Wendy drove at a speed 20 km/h slower than Zoe. Leaving your answer in kilometres,

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

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

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

(b)
Time that Zoe took to travel to the salon
= 3 ÷ 20
= ³₂₀ h

Distance that Zoe travelled
= ³₂₀ x 68
= 10.2 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Wendy's house and the cafe
= 10.2 - 1.5
= 8.7 km

Answer(s): (a) 3 km; (b) 8.7 km