# Speed distance time?

## Feb 17, 2018

If they start moving towards each other simultaneously, they will meet after $1$ hour.

#### Explanation:

If they meet at a distance$x$ from the truck side,

Distance covered by truck will be :

Distance = $x$ = speed x time = $\frac{145}{2.5} \times t$

$\implies x = 58 t$------(1)

Distance covered by car will be :

distance = $145 - x$ = 1.5 times speed of truck x time=

$145 - x$= $1.5 \times \frac{145}{2.5} \times t$

$\implies - x = \frac{145 \times 1.5}{2.5} \times t - 145$

$\implies - x = 87 t - 145$

$\implies x = 145 - 87 t$----(2)

equating (1) and(2):

$58 \times t = 145 - 87 t$

$87 t + 58 t = 145$

$\implies 145 t = 145$

$\implies t = 1$ hour.

Feb 17, 2018

One hour.

#### Explanation:

Using the fact that $d = r t$, we first solve for the speed of the truck.

$145 = 2.5 r$
$58 = r$

The rate of the truck is 58 miles per hour.

Since the car is 1.5 times faster than the truck, the speed of the truck is 1.5×58 or $87$ miles per hour.

Now, if the truck and the car are coming towards each other, then it is the same as combining their speed.

Therefore, $145 = \left(58 + 87\right) t$

$145 = 145 t$
$t = 1$

It takes one hour.