Question

Bruce and Clarke are looking for the shortest route from their home to local donut hangout. Route $A$ is $1.5$ times longer than Route $B$ and $\frac{3}{4}$ the length of Route $C$. If Route $C$ is $3$ km, how much longer is Route $A$ than Route $B$?

• A. $0.75$ km
• B. $1.5$ km
• C. $2$ km
• D. $2.25$ km

Answer 1

The correct option is A $0.75$ km

It is given that the length of route $C$ is $3$km and route $A$ is $\frac{3}{4}$ of route $C$.

Therefore route $A$ is $\frac{3\left(3\right)}{4}$km $=2.25$km.

Now route $A$ is $1.5$ times longer than route $B$.

Let the length of route $B$ is 'B', then $A=1.5B=\frac{3}{2}B$

Hence $B=\frac{2A}{3}$.

But from (i), we know that $A=2.25$ km

Hence, length of route $B$ is

$\frac{2}{3}\times \left(2.25\right)$km $=1.5$km

Therefore the difference in the length of routes $A$ and $B$ is

$A-B=2.25-1.5=0.75$km.