Question

An ostrich can run 5 mph faster than a giraffe. an ostrich can run 5 mi in the same time that a giraffe can run 4 mi. find the speed of each animal.

Answer 1

To answer this you can use a guess and check strategy.

You can start with having the ostrich run 10 mph. If they run 5 mile it would take 1/2 hour.

If the giraffe runs 5 miles per hour, it would run 2.5 miles in half an hour.

You can the double the speed.

If an ostrich runs 20 mph, it would take 1/4 hour to go 5 miles.

The giraffe would run 15 miles per hour so it would travel 1/4 x 15= 3.75 miles. Closer.

Next, if the ostrich runs 25 mph, it will take 1/5 hour to go 5 miles.

If the giraffe runs 20 mph, it will go 4 miles because 1/5 x 20 = 4 miles.

The ostrich's speed is 25 mph, and the giraffe's is 20 mph.

Another way to do this is to write equivalent ratios until the speed are 5 mph apart.

4/5, 8/10, 12/15, 16/20, 20/25.

Answer 2

The first thing we must do in this case is to define variables.
We have then:
x: speed of the giraffe
x + 5: speed of the ostrich

By definition we have:
d = v · t
d / v = t
Where,
d: distance
v: speed
t: time
Since the time is the same then we have:

5 / (x + 5) = 4 / x
5x = 4 (x + 5)
Clearing x we have:
5x-4x = 20
x = 20 mph (speed of the giraffe)
x + 5 = 20 + 5 = 25 mph (speed of the ostrich)
Answer:
20 mph (speed of the giraffe)
25 mph (speed of the ostrich)