Please Help me with this math problem

Question

The distance along a scenic route between two cities is 522 miles. One group of tourists left from the western end of the route at an average speed of 41 miles per hour. Another group left from the eastern end of the route at the same​ time, traveling in the opposite​ direction, with an average speed of 46 miles per hour. How long will it be before the two groups can expect to​ meet?

Answer 1

Hello Claire,

At the time the two groups meet, the distance traveled by the west-side group plus the distance traveled by the east-side group will equal 522 miles (which is the distance between the two cities).

So let's set up the equation based on the previous statement:

if t = time, then: 41t + 46t = 522

87t = 522

Divide both sides by 87 and you get: t = 6

The two groups will meet after 6 hours of travel.

Quick Check:

After 6 hours of travel:

-west-side group traveled: 41*6= 246 miles

-east-side group traveled: 46*6 = 276 miles

246+276 = 522 miles = the distance between the two cities given by the problem.