A park and a museum, 500 m apart, are situated between Zoe's house and Jean's house. The museum is halfway between the two houses
and the park is closer to Jean's house. Zoe and Jean left their homes at the same time and arrived at the park at the same time. Zoe drove at a speed of 62 km/h while Jean drove at a speed 20 km/h slower than Zoe. Leaving your answer in kilometres,
- how much farther did Zoe travel than Jean?
- how far is Jean's house from the museum?
(a)
Let the distance between Zoe's house and Jean's house be 1 d.
Jean travelled =
12 d - 500 m
Zoe travelled =
12 d + 500 m
Distance that Zoe travelled more than Jean
=
12 d + 500 - (
12 d - 500)
=
12 d + 500 -
12 d + 500
= 1000 m
= 1 km
(b)
Time that Zoe took to travel to the park
= 1 ÷ 20
=
120 h
Distance that Zoe travelled
=
120 x 62
= 3.1 km
1000 m = 1 km
500 m = 0.5 km
Distance between Jean's house and the museum
= 3.1 - 0.5
= 2.6 km
Answer(s): (a) 1 km; (b) 2.6 km