A salon and a cafe, 500 m apart, are situated between Yoko's house and Betty's house. The cafe is halfway between the two houses and the salon is closer to Betty's house. Yoko and Betty left their homes at the same time and arrived at the salon at the same time. Yoko drove at a speed of 78 km/h while Betty drove at a speed 15 km/h slower than Yoko. Leaving your answer in kilometres,

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

(a)
Let the distance between Yoko's house and Betty's house be 1 d.
Betty travelled = ¹₂ d - 500 m
Yoko travelled = ¹₂ d + 500 m

Distance that Yoko travelled more than Betty
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Yoko took to travel to the salon
= 1 ÷ 15
= ¹₁₅ h

Distance that Yoko travelled
= ¹₁₅ x 78
= 5.2 km

1000 m = 1 km
500 m = 0.5 km

Distance between Betty's house and the cafe
= 5.2 - 0.5
= 4.7 km

Answer(s): (a) 1 km; (b) 4.7 km