2 distance problems =(...Help

[tRNA]

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Hi all,
I have 2 distance problems that I just don't know how to solve, any help would be greately appreciated and please explain your answer:

1) Trisha ran to the park and then walked home. It took her ½ hour to get to the park and 1 hour and 20 minutes to get home. If she runs 5 miles an hour faster than she walks, how far does she live from the park?

2) an eagle can fly 35 kilometers per hour faster than a hummingbird. In the same amount of time, an eagle can fly 8.5 kilometers and a hummingbird can fly 5 kilometers. How fast can each bird fly?

thanks in advance

 

[Ryltar]

1) Running- 1/2 hour, Walking- 4/3 hour
Let distance from park equal x. Let r be the rate of walking.

Distance = rate * time

Equation for walking x = r (4/3)
Equation for running x = (r+5)(1/2) = r/2 + 5/2
Set them equal:
4r/3 = r/2 + 5/2
8r/6 = 3r/6 + 5/2
5r/6 = 5/2
5r = 30/2 = 15
r = 3 mi/hr

Plugging it back into the walking equation
d = r * t
= (3mi/hr) (4/3hr) = 4 miles

2) Rate eagle = Rate humming bird + 35km/hr
Let r be the rate of the humming bird
d = r * t

5 = r * t

8.5 = (r + 35) * t
8.5 = (r + 35) (5/r)
8.5 = 5r/r + 35/r = 5 + 35/r
3.5 = 35/r
r = 35/3.5 = 10

Thus rate of humming bird = 10km/hr
and rate of the eagle = 45km/hr

 

[potbelly]

2) Rate eagle = Rate humming bird + 35km/hr
Let r be the rate of the humming bird
d = r * t

5 = r * t

8.5 = (r + 35) * t
8.5 = (r + 35) (5/r)
8.5 = 5r/r + 35/r = 5 + 35/r
3.5 = 35/r
r = 35/3.5 = 10

Thus rate of humming bird = 10km/hr
and rate of the eagle = 45km/hr[/quote]

I think you missed the last step..

If you find the rate (r=10) you have to multiply it to 8.5 and 5 respectively.

Thus the answer is

Eagle is 85 km/h and humming bird is 50 km/h

 

[Ryltar]

Whoops I see my mistake, which is corrected in bold.

d = r * t

5 = r * t

8.5 = (r + 35) * t
8.5 = (r + 35) (5/r)
8.5 = 5r/r + 175/r = 5 + 175/r
3.5 = 175/r
r = 175/3.5 = 50
Thus humming bird = 50km/hr
Eagle = 85km/hr