Answer:
The slower motorcycle traveled 720 km.
Step-by-step explanation:
In order to obtain how far the slow one traveled, you have to use the equation [tex]v=\frac{d}{t}[/tex] (I)
where v is the speed,d is the distance and t is the time. Then, you have to use the given relations and solve system of equations.
Let v1 and v2 represent the speed of the faster one and the slower one, respectively.
Let d1,t1 and d2,t2 represent the distance and time traveled by the faster one and the slower one, respectively.
It is known that:
v1=120 km/h
v2=90km/h
t1=4+t2 (because the faster one travels for 4 hours longer than the slower one)
d1=2d2 (because the faster one goes twice as far as the slower one)
Using (I):
[tex]t1=\frac{d1}{v1}[/tex] (II)
[tex]t2=\frac{d2}{v2}[/tex] (III)
Replacing (II) and (III) in t1=4+t2
[tex]\frac{d1}{v1}=4+\frac{d2}{v2}[/tex]
[tex]\frac{1}{120}d1=4+\frac{1}{90}d2[/tex] (IV)
Replacing d1=2d2 in (IV):
[tex]\frac{1}{120}(2)d2= 4+\frac{1}{90}d2\\\frac{1}{60}d2-\frac{1}{90}d2=4[/tex]
Using d2 as common factor:
[tex]d2(\frac{1}{60}-\frac{1}{90})=4[/tex]
Solving the fractions:
[tex]d2(\frac{1}{180})=4[/tex]
Multiplying by 180 both sides:
d2=180(4)=720 km
