A park and a museum, 500 m apart, are situated between Cathy's house and Irene's house. The museum is halfway between the two houses
and the park is closer to Irene's house. Cathy and Irene left their homes at the same time and arrived at the park at the same time. Cathy drove at a speed of 60 km/h while Irene drove at a speed 12 km/h slower than Cathy. Leaving your answer in kilometres,
- how much farther did Cathy travel than Irene?
- how far is Irene's house from the museum?
(a)
Let the distance between Cathy's house and Irene's house be 1 d.
Irene travelled =
12 d - 500 m
Cathy travelled =
12 d + 500 m
Distance that Cathy travelled more than Irene
=
12 d + 500 - (
12 d - 500)
=
12 d + 500 -
12 d + 500
= 1000 m
= 1 km
(b)
Time that Cathy took to travel to the park
= 1 ÷ 12
=
112 h
Distance that Cathy travelled
=
112 x 60
= 5 km
1000 m = 1 km
500 m = 0.5 km
Distance between Irene's house and the museum
= 5 - 0.5
= 4.5 km
Answer(s): (a) 1 km; (b) 4.5 km