An ostrich can run 6 mph faster than a giraffe. An ostrich can run 7 mi in the same time that a giraffe can run 6 mi. Find the speed of each animal.

Question

 An ostrich can run 6 mph faster than a giraffe. An ostrich can run 7 mi in the same time that a giraffe can run 6 mi. Find the speed of each animal.

Answer 1

v1 = speed of ostrich

 

v2 = speed of giraffe

 

Then

 

(i)    v1 = v2 + 6

 

(ii)   v1 * t = 7

 

(iii)  v2 * t = 6

 

Solve these 3 equations in 3 unknowns t, v1, and v2.

 

Plug v1 from (i) into (ii) and get

 

(v2 + 6) * t = 7 ⇒ t = 7 / (v2 + 6)

 

Plug this result for t into (iii) and get

 

v2 * [ 7 / (v2 + 6)] = 6

 

7 v2 = 6  (v2 + 6)

 

v2 = 36

 

Finally, 

 

v1 = v2 + 6 = 36 + 6 = 42

 

t =  7 / (v2 + 6) =  7 / (36 + 6) = 7/42 ≅ 0.1667 

 

Test the answers:

 

v1 * t = 42 (7/42) = 7 (good)

 

v2 * t = 36 (7/42) = 6 (good)

 

v2 + 6 = 36 + 6 = 42 = v1 (good)

 

Ostrich speed is 42 mph

Giraffe speed is 36 mph