A salon and a cafe, 1500 m apart, are situated between Jen's house and Abi's house. The cafe is halfway between the two houses and the salon is closer to Abi's house. Jen and Abi left their homes at the same time and arrived at the salon at the same time. Jen drove at a speed of 66 km/h while Abi drove at a speed 11 km/h slower than Jen. Leaving your answer in kilometres,

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

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

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

(b)
Time that Jen took to travel to the salon
= 3 ÷ 11
= ³₁₁ h

Distance that Jen travelled
= ³₁₁ x 66
= 18 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Abi's house and the cafe
= 18 - 1.5
= 16.5 km

Answer(s): (a) 3 km; (b) 16.5 km