A park and a museum, 1500 m apart, are situated between Eva's house and Dana's house. The museum is halfway between the two houses
and the park is closer to Dana's house. Eva and Dana left their homes at the same time and arrived at the park at the same time. Eva drove at a speed of 65 km/h while Dana drove at a speed 10 km/h slower than Eva. Leaving your answer in kilometres,
- how much farther did Eva travel than Dana?
- how far is Dana's house from the museum?
(a)
Let the distance between Eva's house and Dana's house be 1 d.
Dana travelled =
12 d - 1500 m
Eva travelled =
12 d + 1500 m
Distance that Eva travelled more than Dana
=
12 d + 1500 - (
12 d - 1500)
=
12 d + 1500 -
12 d + 1500
= 3000 m
= 3 km
(b)
Time that Eva took to travel to the park
= 3 ÷ 10
=
310 h
Distance that Eva travelled
=
310 x 65
= 19.5 km
1000 m = 1 km
1500 m = 1.5 km
Distance between Dana's house and the museum
= 19.5 - 1.5
= 18 km
Answer(s): (a) 3 km; (b) 18 km