A salon and a cafe, 1500 m apart, are situated between Jade's house and Emily's house. The cafe is halfway between the two houses and the salon is closer to Emily's house. Jade and Emily left their homes at the same time and arrived at the salon at the same time. Jade drove at a speed of 76 km/h while Emily drove at a speed 19 km/h slower than Jade. Leaving your answer in kilometres,

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

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

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

(b)
Time that Jade took to travel to the salon
= 3 ÷ 19
= ³₁₉ h

Distance that Jade travelled
= ³₁₉ x 76
= 12 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Emily's house and the cafe
= 12 - 1.5
= 10.5 km

Answer(s): (a) 3 km; (b) 10.5 km