A salon and a cafe, 500 m apart, are situated between Julie's house and Usha's house. The cafe is halfway between the two houses and the salon is closer to Usha's house. Julie and Usha left their homes at the same time and arrived at the salon at the same time. Julie drove at a speed of 76 km/h while Usha drove at a speed 19 km/h slower than Julie. Leaving your answer in kilometres,

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

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

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

(b)
Time that Julie took to travel to the salon
= 1 ÷ 19
= ¹₁₉ h

Distance that Julie travelled
= ¹₁₉ x 76
= 4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Usha's house and the cafe
= 4 - 0.5
= 3.5 km

Answer(s): (a) 1 km; (b) 3.5 km