A salon and a cafe, 1500 m apart, are situated between Abi's house and Ivory's house. The cafe is halfway between the two houses and the salon is closer to Ivory's house. Abi and Ivory left their homes at the same time and arrived at the salon at the same time. Abi drove at a speed of 70 km/h while Ivory drove at a speed 10 km/h slower than Abi. Leaving your answer in kilometres,

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

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

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

(b)
Time that Abi took to travel to the salon
= 3 ÷ 10
= ³₁₀ h

Distance that Abi travelled
= ³₁₀ x 70
= 21 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Ivory's house and the cafe
= 21 - 1.5
= 19.5 km

Answer(s): (a) 3 km; (b) 19.5 km