Solve for distance when given 2 speeds and a difference between the 2 in time

Question

I was given a question in math class which asked this question:

Raj went Xkm in 90kmh to go to his work. One day he went 120kmh and shaved 16 minutes off of his regular time. What is X?

I was very confused and just wanted to see how this would be solved.

Answer 1

This seems pretty straightforward.

$V=D/T\rightarrow T=D/V$

So

$T_2-T_1 = D_2/V_2 - D_1/V_1$

Use $D_2=D_1$, simply solve for $D_1$ given the known time difference and the known velocities.

Answer 2

I would naturally set up two equations for $X$ while considering the velocity in $\frac{km}{\color{blue}{min}}$, since the time difference is given as $16 \color{blue}{min}$:

• $90 \frac{km}{h} = \frac{3}{2}\frac{km}{min}$
• $120 \frac{km}{h} = 2\frac{km}{min}$

Now, the equations for $X$ are ($t$ is measured in minutes): $$X = \frac{3}{2}t \mbox{ and } X = 2(t-16)$$

Solving for $X$ gives $\boxed{X = 96km}$