Question

Zach lives in Salina, Kansas. Gina lives 45 miles east in Junction City, Kansas. Gina and Zach both leave their houses at the same time, heading east on I-70. Zach drives 65 miles per hour and Gina drives 55 miles per hour. Zach wants to determine how long it will take before he catches up with Gina.

Answer 1

4.5 hours

Explanation:

Given that Gian lives 45 miles east of Salina where Zach lives.

At the same time, both start driving in the same direction towards the east, Zach drives 65 miles per hour and Gina drives 55 miles per hour.

Let A and B are the initial locations of Zach and Gina respectively, after t hours they meet at point C which x miles east of point B as shown in the figure.

Distance traveled by Gina = BC= x miles

As distance = speed x time, so

`x= 55 * t \cdots(i)`

Similarly, distance traveled by Gina = AC= (45+x) miles

As distance = speed x time, so

`45+x= 65 * t \\\\`

`\Rightarrow 45+55t= 65 * t` [ using equation (i)]

`\Rightarrow 10t= 45 \\\\`

`\Rightarrow t = 45/10 = 4.5` hour

Hence, the required time is 4.5 hours.