A salon and a cafe, 1500 m apart, are situated between Cathy's house and Emily's house. The cafe is halfway between the two houses and the salon is closer to Emily's house. Cathy and Emily left their homes at the same time and arrived at the salon at the same time. Cathy drove at a speed of 64 km/h while Emily drove at a speed 10 km/h slower than Cathy. Leaving your answer in kilometres,

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

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

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

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

Distance that Cathy travelled
= ³₁₀ x 64
= 19.2 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Emily's house and the cafe
= 19.2 - 1.5
= 17.7 km

Answer(s): (a) 3 km; (b) 17.7 km