# A car traveling 95 km/h is 210 m behind a truck traveling 75 km/h. How long will it take the car to reach the truck?

Mar 4, 2017

$t = \text{0.0084 hr}$ or $\text{0.504 min}$ or $\text{30.24 s}$

#### Explanation:

Write the distance as a function of time

${x}_{\text{car}} = 95 t - 0.210$

${x}_{\text{truck}} = 75 t$

You need

${x}_{\text{car" = x_"truck}}$

The two distance functions are equal at the time when the car reaches the truck.

$95 t - 0.210 = 75 t$

$95 t - 75 t = 0.210$

$25 t = 0.210$

$t = \frac{0.210}{25}$

$t = \text{0.0084 hr = 0.504 min = 30.24 s}$