Question

Pierre and Monique leave their home in Portland at the same time. Pierre drives north on the turnpike at a speed of 75 miles per hour while Monique drives south at a speed of 68 miles per hour. How long will it take them to be 429 miles apart?

Short answer

3 hours time it take them to be 429 miles apart

Step-by-step solution

Step 1. Given information

Let tbe the time.

Pierre drives north on the turnpike at a speed of =$75milesperhour$

Monique drives south at a speed of$68milesperhour$

Step 2. finding How long will it take them to be 429 miles apart

Pierre takes time to be 429 miles apart $75\times t=75t$

Monique takes time to be 429 miles apart $68\times t=68t$

The distance traveled by the Pierre going north plus the distance travelled by the Monique going south must add up to 429 miles

So,we write it as $75t+68t=429$

$$\begin{gathered} 143t=429 \\ t=\frac{429}{143} \\ t=3 \end{gathered}$$

3 hours time it take them to be 429 miles apart

Pierre takes time to be 429 miles apart$75\times 3=225miles$

Monique takes time to be 429 miles apart$68\times 3=204miles$