Answer:
From city A to city B her speed was 38 mi/h
Step-by-step explanation:
The traveled distance can be calculated using this equation:
From city A to city B
228 mi = v · t₁
Where:
v = velocity
t₁ = time it took Kiran to travel the 228 mi from city A to city B
From city B to city C
400 mi = (v + 12 mi/h) · t₂
We also know that the entire trip took 14 h, then:
t₁ + t₂ = 14 h
So, we have a system of three equations with three unknwons:
228 mi = v · t₁
400 mi = (v + 12 mi/h) · t₂
t₁ + t₂ = 14 h
Let´s solve the third equation for t₁:
t₁ = 14 h - t₂
Now let´s replace t₁ in the first equation and solve it for t₂
228 mi = v · t₁
228 mi = v · (14 h - t₂)
228 mi/v - 14 h = - t₂
t₂ = 14 h - 228 mi/v
Now let´s replace t₂ in the second equation:
400 mi = (v + 12 mi/h) · t₂
400 mi = (v + 12 mi/h) · (14 h - 228 mi/v)
400 mi = 14 h · v - 228 mi + 168 mi - 2736 mi²/(v · h)
400 mi = 14 h · v - 60 mi - 2736 mi²/(v · h)
460 mi = 14 h · v - 2736 mi²/(v · h)
Multiplicate by v both sides of the equation:
460 mi · v = 14 h · v² - 2736 mi²/h
0 = 14 h · v² - 460 mi · v - 2737 mi²/h
Solving the quadratic equation:
v = 38 mi/h
(The other solution of the equation is negative, and therefore discarded)
From city A to city B her speed was 38 mi/h