A salon and a cafe, 2500 m apart, are situated between Zoe's house and Kimberly's house. The cafe is halfway between the two houses and the salon is closer to Kimberly's house. Zoe and Kimberly left their homes at the same time and arrived at the salon at the same time. Zoe drove at a speed of 76 km/h while Kimberly drove at a speed 19 km/h slower than Zoe. Leaving your answer in kilometres,

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

(a)
Let the distance between Zoe's house and Kimberly's house be 1 d.
Kimberly travelled = ¹₂ d - 2500 m
Zoe travelled = ¹₂ d + 2500 m

Distance that Zoe travelled more than Kimberly
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Zoe took to travel to the salon
= 5 ÷ 19
= ⁵₁₉ h

Distance that Zoe travelled
= ⁵₁₉ x 76
= 20 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Kimberly's house and the cafe
= 20 - 2.5
= 17.5 km

Answer(s): (a) 5 km; (b) 17.5 km