A salon and a cafe, 3500 m apart, are situated between Zara's house and Raeann's house. The cafe is halfway between the two houses and the salon is closer to Raeann's house. Zara and Raeann left their homes at the same time and arrived at the salon at the same time. Zara drove at a speed of 62 km/h while Raeann drove at a speed 20 km/h slower than Zara. Leaving your answer in kilometres,

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

(a)
Let the distance between Zara's house and Raeann's house be 1 d.
Raeann travelled = ¹₂ d - 3500 m
Zara travelled = ¹₂ d + 3500 m

Distance that Zara travelled more than Raeann
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Zara took to travel to the salon
= 7 ÷ 20
= ⁷₂₀ h

Distance that Zara travelled
= ⁷₂₀ x 62
= 21.7 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Raeann's house and the cafe
= 21.7 - 3.5
= 18.2 km

Answer(s): (a) 7 km; (b) 18.2 km