Rational Expressions

Question

A truck loaded with ostriches is traveling 20km/h faster than a freight train carrying emus. In the time it takes the train to travel 160km, the truck travels 240km. Determine algebraically the speed the speed of the truck

Answer 1

Speed equals distance divided by time, so speed multiplied by time equals distance, let V be speed of train, then V + 20 would be speed of truck so

(V + 20)t = 240 ; V•t = 160 [solve for t] t = 160/V substitute for t in first equation (V + 20)160/V = 240

multiply both sides by V so (V +20)160 =240V ; 160V + 3200 = 240V ; 3200 = 80V; V=40 km/hr

so truck’s speed 40 + 20 = 60 km/hr

Answer 2

Let t = speed of train (km/h)

speed of truck = t+20 (km/h)

over time x, train travels 160 km and truck travels 240km

tx = 160

(t+20)x - 240 ⇒x = 240/(t+20)

substituting for x into the first equation

t(240/(t+20)) = 160

240t = 160(t+20)

240t = 160t + 3200

80t = 3200

t = 40

So speed of train is 40km/h and speed of truck is 60 km/h