A salon and a cafe, 1500 m apart, are situated between Zara's house and Irene's house. The cafe is halfway between the two houses and the salon is closer to Irene's house. Zara and Irene left their homes at the same time and arrived at the salon at the same time. Zara drove at a speed of 69 km/h while Irene drove at a speed 20 km/h slower than Zara. Leaving your answer in kilometres,

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

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

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

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

Distance that Zara travelled
= ³₂₀ x 69
= 10.35 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Irene's house and the cafe
= 10.35 - 1.5
= 8.85 km

Answer(s): (a) 3 km; (b) 8.85 km