Help: Math problem with quadratic equation

Question

A cheetah travels 40 kmph faster than a lion. The cheetah goes 360 km in 3 hours less time than the lion goes 360 km. Find the speed of each animal

Answer 1

Let C = Cheetah's speed

and let L = Lion's speed

C=L+40 Then use the d=rt formula for distance distance = rate of speed x time

d/r=t

360/C=360/L - 3

substitute C=L+40 into above equation

360/(L+40) = 360/L -3

Simplify and solve for L

Multiply both sides by (L+40)L to get

360L = 360(L+40) - 3(L+40)L

360L = 360L + 14400 - 3L² -120L

3L² +120L - 14400 = 0

divide by 3

L² +40L - 4800 = 0

Complete the square, take half of 40 and square it, to get 400. Add & subtract 400:

L² + 40L +400 - 4800 - 400 = 0

(L+20)² -5200 = 0

(L+20)² = 5200

take square root of both sides

L+20 = 20(13)^1/2

L=20(13)^1/2 - 20 = 20[13)^1/2-1] = about 20(3.61-1) = 20(2.61) = 52.2 kmph

C= 40 + 52.2 = 92.2 kmph

The cheatah does 360 km in 360km/92.2 kmph = 3.9 hours

the lino does 360 km in 360km/52.2 kmph = 6.9 hours