Question

* Two cars started to move from C (118miles) and from D(256 miles), towards one another. The car that starts at point C moves twice as fast as the car that starts at point D. How far from Boston will these two cars meet?

Answer 1

Answer:

They meet at 92 miles from C or 46 miles from D.

Step-by-step explanation:

Constant Speed Motion

An object is said to have constant speed if it travels the same distance at the same time. The ratio between the distance x and the time t is the speed and is given by

$\displaystyle v=\frac{x}{t}$

Solving for x

$x=v.t$

The car starting from C has double speed as the car starting from D. this means

$v_c=2v_d$

When both cars meet, they travel these distances

$x_c=v_c.t$

$x_d=v_d.t$

The sum of both distances is x = 256 - 118 = 138 miles.

$x_c+x_d=138$

Or, equivalently

$v_c.t+v_d.t=138$

Using the relations of the speeds:

$2v_d.t+v_d.t=138\\3v_d.t=138$

Solving for t

$\displaystyle t=\frac{138}{3v_d}=\frac{46}{v_d}$

The distance traveled by the car from c is

$\displaystyle x_c=2.v_d\frac{46}{v_d}=92\ miles$

The distance traveled by the car from d is

$\displaystyle x_d=v_d\frac{46}{v_d}=46\ miles$

There is no reference of where Boston is located, thus we can only refer the distances respect to C or D, as shown above