A salon and a cafe, 500 m apart, are situated between Xandra's house and Jean's house. The cafe is halfway between the two houses
and the salon is closer to Jean's house. Xandra and Jean left their homes at the same time and arrived at the salon at the same time. Xandra drove at a speed of 78 km/h while Jean drove at a speed 10 km/h slower than Xandra. Leaving your answer in kilometres,
- how much farther did Xandra travel than Jean?
- how far is Jean's house from the cafe?
(a)
Let the distance between Xandra's house and Jean's house be 1 d.
Jean travelled =
12 d - 500 m
Xandra travelled =
12 d + 500 m
Distance that Xandra travelled more than Jean
=
12 d + 500 - (
12 d - 500)
=
12 d + 500 -
12 d + 500
= 1000 m
= 1 km
(b)
Time that Xandra took to travel to the salon
= 1 ÷ 10
=
110 h
Distance that Xandra travelled
=
110 x 78
= 7.8 km
1000 m = 1 km
500 m = 0.5 km
Distance between Jean's house and the cafe
= 7.8 - 0.5
= 7.3 km
Answer(s): (a) 1 km; (b) 7.3 km